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Max’s Cool Beans By Max the Magnificent Arduino Bootcamp – Part 22 (more on BCD & other stuff) A s usual, my head is bursting with all sorts of “stuff” I want to talk about. For example, a young engineer recently contacted me to say he was in the process of writing a technology-related book about something or other (I don’t want to give the game away). He was asking for advice regarding potential publishers. I know how hard it can be to get one’s foot through the publishing door, especially in the case of older, staid companies whose revolving doors have a habit of leaving you on the outside with your nose pressed against the glass looking in. Happily, I was able to recommend the guys and gals at No Starch Press, who bill themselves as “The finest in geek entertainment” (https://nostarch.com/). To be honest, I cannot remember seeing a No Starch publication I didn’t want to add to my library. Their Learn to Program with Minecraft by Craig Richardson is awesome. Some of the other No Starch tomes that grace my bookshelves are Dead Simple Python: Idiomatic Python for the Impatient Programmer by Jason C. McDonald, Computer Architecture: From the Stone Age to the Quantum Age by Charles Fox, and The Game Console 2.0: A Photographic History from Atari to Xbox by Evan Amos. Also, I just took delivery of Writing a C Compiler: Build a Real Programming Language from Scratch by Nora Sandler. Now, before we expand on our previous discussions and take a deeper dive into the binary-coded decimal (BCD) waters, a couple of other topics are bouncing around my old noggin. So, if you will be kind enough to indulge me… Feeling grey or gray? The fact that some words have different spellings in British English (I hail from the UK) and American English (I currently hang my hat in the USA) can be a tad tiresome. For example, ‘grey’ is more common in British banter, while ‘gray’ is more frequent in American argot. By some strange quirk of fate, this leads us to the topic of Frank Gray (1887–1969), who was a physicist and researcher at Bell Labs. Frank was responsible for numerous innovations, especially in the field of television. However, he is primarily remembered for coming up with the concept of Gray codes (when I started out, I wondered why they weren’t called “Grey codes”). Connection Binary 0 0 0 0 0 0 1 0 0 1 0 0 1 2 0 1 0 0 1 1 3 0 1 1 0 1 0 4 1 0 0 1 1 0 5 1 0 1 1 1 1 6 1 1 0 1 0 1 7 1 1 1 1 0 0 Fig.1: Binary vs. Gray codes. 46 As that philosopher for our time, Mickey Mouse (1928–) famously said: Display segments and pin numbers Ground (0V) D9 D0 D1 5 10 9 1 2 4 6 7 DP G F E D C B A Gray 0 Count on me No connection 3 Decimal Compare and contrast the two 3-bit sequences shown in Fig.1, for example. In the case of transitions between 1 and 2 or 5 and 6 in decimal, two bits change when using a standard binary counting sequence. Similarly, in the case of transitions between 3 and 4 or 7 and 0 in decimal, all three bits change in standard binary. By comparison, the ordering of the values in the Gray code are such that adjacent values always differ by only a single bit. In addition to their use when arranging the rows and columns in Karnaugh maps, Gray codes are widely employed to prevent spurious outputs from electromechanical switches and to facilitate error detection and correction in digital communications. 3 C 3 C B B E C B E 10-Bit Ring Counter y9 E y0 INIT CLK From Arduino May or may not be used From Arduino or BCD decoder Fig.2: Using a 10-bit ring counter to control ten 7-segment displays. Practical Electronics | October | 2024 “Arithmetic is being able to count up to twenty without taking off your shoes”. You can’t argue with logic like that. In my last column, we discussed how we could use ten D-type flip-flips to implement a 10-bit ring counter. The idea is that only one bit from this counter is active (logic 1) at any time, so clocking the counter results in a sequence of 1000000000, 0100000000, 0010000000… 0000000100, 0000000010, 0000000001, and back to 1000000000 again. As illustrated in Fig.2, we could use the outputs from our ring counter to control ten transistors. In turn, these transistors could control ten 7-segment displays. Personally, I think this is rather clever. When used in conjunction with a BCD decoder, it means we can control all ten 7-segment displays using just six of the Arduino’s pins. Is there any way we could increase our cleverness quotient? Well, by golly, I’m glad you asked because there certainly is. sidering thus far is Straight JohnsonCounter Counter StraightRing RingCounter Counter Johnson a ‘straight ring counState Q0 Q0Q1 Q1Q2 Q2Q3 Q3Q4 Q4 State Q0 Q0Q1 Q1Q2 Q2Q3 Q3Q4 Q4 State ter’. It may also be State referred to as a ‘one00 11 00 00 00 00 00 00 00 00 00 00 hot counter’ because 11 00 11 00 00 00 11 11 00 00 00 00 only one output is active, or ‘hot’, at any 22 11 11 00 00 00 22 00 00 11 00 00 time. A comparison 33 11 11 11 00 00 33 00 00 00 11 00 of 5-bit (aka 5-stage) straight ring and 44 11 11 11 11 00 44 00 00 00 00 11 Johnson counters is 55 11 11 11 11 11 00 11 00 00 00 00 shown in Fig.3. Can you spot the two big 66 00 11 11 11 11 11 00 11 00 00 00 differences between 77 00 00 11 11 11 22 00 00 11 00 00 these implementa88 00 00 00 11 11 33 00 00 00 11 00 tions? The first differ99 00 00 00 00 11 44 00 00 00 00 11 ence derives from the 00 00 00 00 00 00 00 11 00 00 00 00 wiring of the INIT signal. In the case Fig.4: 5-bit straight ring vs Johnson counter sequences. of the straight ring counter, this signal is connected to the the case of the Johnson counter, the D0 S (set) input of the first stage and the R input is fed from QB4, which is the false (reset) inputs of the remaining stages. output from the final stage. This means that when the INIT signal Imagine taking a strip of paper and is placed in its active state, our 5-bit joining its ends to form a circular band. Jolly Japes with Johnsons straight ring counter will be loaded In this case, the band will have two faces I love digital logic. I stand in awe of with a value of 10000. By comparison, or sides (inside and outside) and two people like Frank Gray who can come in the case of the Johnson counter, this edges. This would be the equivalent up with logical concepts like Gray signal is connected to the R inputs of all to our straight ring counter. If we take codes ­– things I wouldn’t be capable of the stages. As a result, when the INIT another strip of paper and give one of conceiving myself in a thousand years. signal is placed in its active state, our its ends a one-half twist before joining Another of my heroes is the American 5-bit Johnson counter will be loaded the two ends, we end up with a Möbius inventor, engineer, computer pioneer with a value of 00000. strip, which boasts only one side and and professor, Robert Royce “Bob” The second difference occurs in the one edge. This would be the counterpart Johnson (1928–2016). Amongst many way in which we feed the inputs to our to our Johnson counter. other inventions and innovations, Bob counters. In the case of the straight ring The way in which we implement the came up with something we now call counter, the D0 input to the first stage feedback path in our Johnson counter is fed from Q4, which is the true output explains why this form of counter may the Johnson counter. The ring counter we’ve been con- from the final stage. By comparison, in also be referred to as a ‘twisted ring Connection No connection counter’, a ‘switch-tail ring counter’, a ‘walking ring counter’, or a ‘Möbius counter’ (good luck finding tidbits of trivia like this in other, lesser electronic S S S S S D0 Q0 D1 Q1 D2 Q2 D3 Q3 D4 Q4 hobbyist magazines!). So, how do these seemingly trivial QB0 QB1 QB2 QB3 QB4 differences affect the outputs of these R R R R R counters in the real world? The easiest way to wrap our brains around this is INIT to compare the number of count states CLK along with their corresponding values as proffered by these dueling implementations (Fig.4). y0 y1 y2 y3 y4 As we see, there are multiple dif(a) 5-stage straight ring counter ferences in the sequences. A glance at the highlighted 1s in Fig.4 reveals that the straight ring counter circulates a S S S S S single 1 bit around the ring (it could be D0 Q0 D1 Q1 D2 Q2 D3 Q3 D4 Q4 a 0 if we wished). By comparison, the Johnson counter circulates a stream of QB0 QB1 QB2 QB3 QB4 R R R R R 1s followed by a stream of 0s. A by-product of the previous point INIT is that, in the case of the straight ring CLK counter, two bits always change when transitioning from one state to the next. By comparison, in the case of the Johny0 y1 y2 y3 y4 son counter, only a single bit changes (b) 5-stage Johnson counter when transitioning from one state to the Fig.3: 5-bit straight ring vs. Johnson counter implementations. next. This means the Johnson counter Practical Electronics | October | 2024 47 Each of his register states was imDecoded Outputs plemented using y0 = Q0B & Q1B & Q2B & Q3B & Q4B 0 0 0 0 0 0 two back-to-back tubes. So, instead y1 = Q0 & Q1B & Q2B & Q3B & Q4B 1 1 0 0 0 0 of using 20 expeny2 = Q0 & Q1 & Q2B & Q3B & Q4B 2 1 1 0 0 0 sive tubes to build a 10-bit straight y3 = Q0 & Q1 & Q2 & Q3B & Q4B 3 1 1 1 0 0 ring counter, Johny4 = Q0 & Q1 & Q2 & Q3 & Q4B 4 1 1 1 1 0 son required only y5 = Q0 & Q1 & Q2 & Q3 & Q4 5 1 1 1 1 1 10 tubes to build his 5-bit counter. y6 = Q0B & Q1 & Q2 & Q3 & Q4 6 0 1 1 1 1 Furthermore, each y7 = Q0B & Q1B & Q2 & Q3 & Q4 7 0 0 1 1 1 of his ten 5-input AND gates was imy8 = Q0B & Q1B & Q2B & Q3 & Q4 8 0 0 0 1 1 plemented cheaply y9 = Q0B & Q1B & Q2B & Q3B & Q4 9 0 0 0 0 1 and cheerfully Fig.5: Decoding 10 one-hot signals from a 5-bit Johnson counter. using only one resistor and five is implementing a form of Gray code. diodes. Pretty clever, eh? And, speaking of states, the 5-bit While this discussion isn’t particularly straight ring counter passes through relevant to what we aim to achieve, in only five states (numbered 0 to 4) before my experience, being aware of concepts returning to its starting state. We could like this can be unexpectedly useful generalize this to say that an n-bit straight when one least expects it. ring counter passes through n states How common! before returning to its starting state. Before returning to the BCD fray, we By comparison, the 5-bit Johnson counter passes through ten states (0 to must take one more little diversion (so 9) before returning to its starting state. unlike me, I know); some of the things We could generalize this to say that an we are going to talk about shortly can n-bit Johnson counter passes through 2n be hard to wrap one’s brain around, it states before returning to its starting state. behooves us to take things step-by-step. Throughout this epic Arduino BootWe’ve already seen how to control ten 7-segment displays using a 10-bit camp series, we’ve been working with straight ring counter. The cool thing is common-cathode (CC) 7-segment disthat, since we get both the Q (true) and plays, as shown in Fig.6(a). This means QB (false) outputs from each register the cathodes associated with the eight stage ‘for free’, we can achieve the same light-emitting diode (LED) segments thing using a 5-bit Johnson counter in are joined inside the device. We use conjunction with ten 5-input AND gates, the anodes to control the LEDs on an as illustrated in Fig.5. individual basis. When the states of 5-bit Johnson counIt’s also possible to get common-anode ter are decoded to generate ten one-hot (CA) 7-segment displays, shown in outputs, the resulting implementation Fig.6(b). In is known as a Johnson Decade Counter. this case, the From Arduino These are available as off-the-shelf chips, anodes are insuch as the 74HC4017 (https://pemag. ternally joined au/link/abzh). and we use Why go to all this trouble? When the cathodes Johnson originally patented this concept to control the in 1954, he was working with diodes, LEDs individ0V resistors, and vacuum tubes (valves). ually. Johnson Counter State Johnson Decade Counter Q0 Q1 Q2 Q3 Q4 Multiple anodes If you cast your mind back to our early experiments with our CC displays, you will recall that we connected our common cathode to ground and used our Arduino to control the anodes (via current-limiting resistors), as in Fig.7(a). As we discussed way back in the mists of time (PE, March 2023), LOW and HIGH in our programs are seen by the compiler as being the same as 0 and 1, respectively. When we write a LOW (or 0) to a digital pin, this will be presented as 0V to the outside world. When we write a HIGH (or 1) to a digital pin, this will be presented as 5V to the outside world (at least, in the case of the Arduino Uno we’re using). In the case of our CC displays, presenting 0V (LOW) or 5V (HIGH) to an anode will switch that segment off or on, respectively. This explains why we’ve been using the following definitions in our programs: // Definitions for CC display #define SEG_ON HIGH #define SEG_OFF LOW Later, in the body of our programs, when we called the digitalWrite() function to instruct one of the Arduino’s pins to switch a segment on or off, we used our SEG_ON and SEG_OFF definitions as arguments to the function. Have you ever wondered why we bothered to create and use these definitions in the first place? Since we intend to use only CC displays in this series, you might feel this is redundant. There are two reasons we typically do it this way. First, even if we only ever use CC displays, the SEG_ON and SEG_OFF names are easy for others to understand if they read our programs (and for us to (b) CA tied to power 5V (a) CC tied to ground From Arduino From Arduino (d) CA with PNP transistor 5V E B PNP C (a) Common cathode (CC) (b) Common anode (CA) C B NPN E 0V Multiple cathodes Fig.6: Common cathode vs common cathode displays. 48 (c) CC with NPN transistor From Arduino Fig.7: CC and CA displays with and without transistors. Practical Electronics | October | 2024 understand when we return long after we’ve forgotten how everything works). Second, if we ever decided to exchange our displays for their pincompatible CA counterparts, as in Fig.7(b), all we have to do on the hardware side would be to disconnect the common pin from 0V (ground) and reconnect it to 5V (power). Meanwhile, on the software side, we just need to modify our definitions as follows: // Definitions for CA display #define SEG_ON LOW #define SEG_OFF HIGH The rest of the program will continue to work ‘as is’. Brilliant! Switcheroo Before we proceed, let’s take a moment to remind ourselves that pure silicon is an insulator. We can modify the silicon using a process called ‘doping’ to add small quantities of different elements into its crystalline matrix. We can create P-type (positive) and N-type (negative) silicon, both of which do conduct. The interesting stuff happens at a PN junction, where P-type and N-type materials meet. A single PN junction forms a diode, a component that only conducts in one direction. If we use the right materials, we end up with a diode that emits light when it’s conducting, ie, a light-emitting diode (LED). If we create a silicon sandwich from two back-to-back PN junctions, we have a bipolar junction transistor (BJT). These components can be used in two ways: as analog amplifiers or as digital switches. Furthermore, there are two ways in which we can create our silicon sandwiches: NPN or PNP (all of this is explained in excruciating exhilarating detail in my book, Bebop to the Boolean Boogie (https://pemag.au/link/abzi). Returning to our common-cathode implementation, in our more recent experiments, we’ve inserted an NPN transistor between the common cathode pin on our 7-segment display and the 0V (ground) rail, as in Fig.7(c). This transistor acts as a switch to simultaneously enable or disable all the segments the Arduino is trying to switch on. The transistor we opted to use was a BC337 because this can handle up to 800mA, much more than maximum current (8 × 20mA = 160mA) if all eight segments are active at the same time. First, we used one of these transistors to control the brightness of a single 7segment display by switching its segments on and off very quickly while controlling the ratio of the on-to-off times (PE, January 2024). Next, we used two of these transistors to multiplex between two 7-segment displays (PE, Practical Electronics | October | 2024 April and May 2024). More recently (starting in PE, June 2024), we moved to using four transistors to multiplex between four 7-segment displays. In our circuits, the signals driving our transistors’ base (B) control terminals come (via current-limiting resistors) from the Arduino. In the case of an NPN transistor used, as in Fig.7(c), 0V on its base will switch it off (like opening a switch), thereby disconnecting the display’s common cathode pin from the 0V rail and ensuring all the display segments are off. By comparison, a 5V signal on the base resistor will switch the transistor on (like closing a switch), thereby connecting the display’s common cathode pin to the 0V rail and activating any segments with 5V on their anode terminals. If we wished to perform similar experiments with a common-anode display, we would use a PNP transistor as illustrated in Fig.7(d). In this case, we might opt for a BC327 (there are, of course, many other candidates for the job). This works in a complementary fashion to its NPN counterpart. In this case, a 0V signal applied to the transistor’s base resistor will switch it on, thereby connecting the display’s common anode pin to the 5V rail and activating any segments with 0V on their cathode terminals. By comparison, a 5V signal applied to the transistor’s base will switch it off, thereby disconnecting the display’s common anode pin from the 5V rail and ensuring all the display segments are off. Want an easy way to remember which symbol is which? Refer to the direction of the arrow at the transistor’s emitter terminal: NPN = Not Pointing iN PNP = Point iN Please DIY or off the shelf? Finally, we are ready to add a BCD to 7-segment decoder to our circuit (Fig.8). In this case, we are going to employ the simplest form of BCD code, known as Natural BCD (NBCD), Simple BCD (SBCD) or 8421 BCD (see last month’s column for more on this). We’ve changed from using uppercase letters A, B, C, D, E, F, G to lowercase a, b, c, d, e, f, g to refer to the segments on our 7-segment display. This is because we are now using the uppercase A, B, C, D characters to refer to the inputs to our BCD decoder. It’s not my fault; I’ll explain more in a moment. When it comes to implementing our BCD decoder, we have a choice: DIY (do it yourself) or off the shelf. By DIY, I mean that, similar to how we realized our 2:4 decoder, we could use a bunch of primitive logic gates (NOT, AND, OR, etc) to implement it. We’d start by thinking of the decoder as a black box, then create a truth table showing the gazins and gazouts. Next, we’d use techniques like Boolean algebra, De Morgan transformations and Karnaugh maps to determine which logic gates to use. Once again, all of this is discussed in Bebop to the Boolean Boogie. The No connection Connection D3 Ground (0V) D2 D0 D1 Display segments and pin numbers 5 10 9 1 2 4 6 7 dp g f e d c b a 3 3 3 3 C C C C B B E B E Fig.8: Adding a BCD-to7-segment decoder. B E y3 y2 y1 y0 Unused g f e d c b a 8421 BCD Decoder 2:4 Decoder s1 s0 Free 13 12 E D C B A Free 11 10 9 8 7 6 5 4 3 2 Arduino pin numbers 49 B 1 16 VCC C 2 15 f ? 3 14 g ? 4 13 a ? 5 12 b D 6 11 A 7 GND 8 From Arduino Inputs Decimal D C B 0 L L 1 L L 2 L L 3 L L c 4 L H 10 d 5 L 9 e 6 L 7 To Displays Fig.9: A top view of the 74LS48N package. problem is that this would take time and effort and I’m feeling lazy today. The alternative is to use an off-the-shelf part like the SN74LS48N. I just found a pack of 10 for £5 on Amazon’s UK website (https://pemag.au/link/abzj), but you can get these little scamps from any major component supplier. As we discussed in an earlier column (PE, August 2024), the “SN” indicates that Texas Instruments (TI) is the manufacturer, the “74” tells us we are working with a commercial component (as opposed to industrial or military), the “LS” informs us that this is a member of the Low-Power Schottky family, the “48” is the type of logic function (a BCD decoder), and the “N” indicates it is in a plastic dual in-line package (PDIP). Data sheet deliriums It’s when we come to cast our orbs over the data sheet for the 74LS48 that things have the potential to get a little confusing (https://pemag.au/link/abzk). Whoever was charged with creating the original version of this little rascal back in the 1970s was overly enthusiastic because they made it their mission to cover a wide variety of parts, packages and functions in this one document. We are focusing on the 74LS48 because this device is intended to drive a common-cathode 7-segment display, which means its outputs are active-high. Its 74LS47 counterpart, also embraced by the same data sheet, has activelow outputs and is designed to drive a common-anode 7-segment display. Based on this data sheet, a representation of the 16-pin package we’re using is presented in Fig.9. This explains why we transitioned to using A, B, C, D characters for the inputs to the decoder and a, b, c, d, e, f, g characters for the signals driving our 7-segment displays. Outputs A a b c d e f g L L H H H H H H L L H L H H L L L L H L H H L H H L H H H H H H H L L H L L L H H L L H H H L H H L H H L H H H H L L L H H H H H L H H H H H H L L L L 8 H L L L H H H H H H H 9 H L L H H H H L L H H 10 H L H L L L L H H L H 11 H L H H L L H H L L H 12 H H L L L H L L L H H 13 H H L H H L L H L H H 14 H H H L L L L H H H H 15 H H H H L L L L L L L Fig.10: The 74LS48 truth table. The GND pin (pin 8) connects to the 0V ground rail on our breadboard, while the VCC power pin (pin 16) will connect to the +5V power rail. The “?” for pins 3, 4, and 5 is because we will consider the functioning of these pins next month. For the moment, we simply use a 10kΩ resistor to disable these pins by pulling them up to logic 1 (the 5V rail). A cut-down version of the truth table from Table T2 in the data sheet is shown in Fig.10 (we’ve omitted pins 3, 4, and 5). In our previous columns, we’ve predominantly used 0s and 1s in our truth tables (along with occasional “X” characters to indicate ‘Don’t Care’ values on the inputs and “?” characters to indicate ‘Don’t Know’ values on the outputs). In the past, it was not uncommon to use “L” and “H” instead of 0 and 1, respectively. I’m continuing to use “L” and “H” here to match the data sheet and because you might run across this sort of thing in the future. Although this isn’t a concern here, it’s worth noting that some truth tables might have “OFF” and “ON” values for their outputs. Oftentimes, this is because the creators of the data sheet were trying to cover multiple device variants, some with active-high outputs and others with active-low outputs. Using “OFF” and “ON” values allows one truth table to cover both implementations. One final point of interest from our truth table arises when we consider the numerical designations and resultant displays illustrated in Fig.11. The numbers 0 through 9 are displayed as we would expect, but what about 10 through 15? We introduced hexadecimal (base 16) in PE, May 2023. Did the designers of this device miss their opportunity to come up with a hexadecimal display? Well, yes and no. On the one hand, many people in the computer industry used only octal (base 8) and decimal (base 10) notations into the late 1970s and early 1980s, and the octal characters (0 to 7) form a subset of the decimal characters (0 to 9). On the other hand, starting in the early 1960s, it became increasingly common to use hexadecimal (base 16) notation. So displaying the hex A, B, C, D, E, F characters would almost certainly have been considered by its designers. The telling point here is the fact that number 15 corresponds to all the segments being off. That is useful if we wish to blank leading zeros on a multi-digit display. We introduced this concept in PE, August 2024, and we will be discussing it in more detail next month. That leaves us with the displays corresponding to numbers 10 through 14. Were these cryptic segment patterns carefully selected by the device’s designers? Do they have some long-forgotten meanings? Personally, I doubt it. I guess that the designers focused on getting the displays they desired for numbers 0 through 9, along with the blank (all segments off) corresponding to number 15, leaving the displays corresponding to numbers 10 through 14 to fall out as they might (I’d love to hear if you have another theory or know something to the contrary). Preparing to add the BCD decoder Before we add the 74LS48 BCD decoder to our breadboard, let’s remind ourselves as to the current state of play. As usual, you can download a PDF of our latest and greatest breadboard, component, and wiring ensemble (file “CBOct24-01.pdf”).All the files mentioned in this column are available from the October 2024 page of the PE website: https://pemag.au/link/abzl To make sure everything is still working before making any changes, let’s load and run our most recent program, which displays the time while suppressing any leading 0 in the most-significant (left- a f g e b c d 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Fig.11: Segment identification, numerical designations and resultant displays from the 74LS48 data sheet. 50 Practical Electronics | October | 2024 Bringing-up the BCD decoder Based on our previous experiences of things not always working as planned the first time around, we will take things step by step. Practical Electronics | October | 2024 dp g f e d c b a To Displays dp g f e d c b a Upper Breadboard 74LS48 16 15 14 13 12 11 10 9 390Ω Lower Breadboard Breakout board 1 2 3 4 5 6 7 8 Resistor pack f g a b c d e 74LS48 BC? ? ?DA 9 8 7 6 5 4 3 2 (a) Without BCD decoder 5 4 3 2 From Arduino (b) With BCD decoder Fig.12: Adding the BCD decoder chip to our breadboard. followed by a red wire from pin 16 (VCC) First, unplug the USB cable from your Arduino to power it down. While to the upper +5V power rail. Also, add working on an antistatic mat and wear- the 0.1µF (100nF) ceramic capacitor ing an antistatic wrist strap, discon- and the 10kΩ pull-up resistor, along nect the breadboard ends of the wires with the three purple wires connected connected to pins 2, 3, 4, and 5 on the to pins 3, 4, and 5. Now reconnect the USB cable from Arduino. Also, completely remove the wires connected to (a) Add 74LS38 (b) Connect Arduino pins 6, 7, 8, and 9 on the Arduino. Now replace the original 150Ω BOB with your new 390Ω BOB or resistor pack on the upper breadboard (remember to con74LS48 74LS48 nect pin 1 on the resistor pack/BOB to ground). Next, add the SN74LS48 IC to the lower breadboard, as in Fig.13(a). Also add Logic probe connection point a black wire from From Arduino 5 4 3 2 pin 8 (GND) to the Fig.13: Upgrading our breadboard one step at a time. lower ground rail, Lower Breadboard most) digit (file “CB-Oct24-02.txt”). If everything is working as expected, we can proceed. The area of interest to us with respect to our existing implementation sans BCD decoder is illustrated in Fig.12(a). As you will recall, since we are multiplexing our displays, this allows us to connect the LED segments from all four displays in parallel (side-by-side). We’re using digital output pins 2 through 9 from the Arduino to drive display segments ‘a’ through ‘f’ and the decimal point (‘dp’), respectively. We are currently using eight 150Ω discrete (individual) current-limiting resistors mounted on a small breakout board (BOB). We discussed its creation in PE, July 2024. Now we will swap out the currentlimiting resistors with new values and add the BCD decoder as illustrated in Fig.12(b). From previous columns we know the red LEDs in our 7-segment displays have a forward voltage drop (VF) of 2V and a maximum forward current (IF) of 20mA (we discussed the concept of a diode’s forward voltage drop in PE, March 2024). The data sheet for the 74LS48 states that the maximum current each output can provide is only 6mA, so that is what we have to work with. Remember that we have NPN transistors in series with each of our displays. These have a ‘saturation voltage’ that appears across them when they are switched on, usually a fraction of a volt. This means that we end up with only about 5V – 2V – 0.5V = 2.5V driving each LED. Using Ohm’s law of V = I × R and rearranging the terms to give R = V ÷ I, we end up with R = 2.5V ÷ 0.006A = 416Ω. The closest standard value to this is 390Ω, which is close enough. You can either build a new BOB or do what I did, which is to use a 16-pin package containing eight isolated 390Ω resistors. These components are created by a variety of manufacturers, like the Bourns 4100R Series (https://pemag.au/ link/abzm), and they are available from most major component vendors, like DigiKey (https://pemag.au/link/abzn). Since we can’t control the decimal point (‘dp’) segments on our 7-segment displays using our BCD decoder, we will connect pin 1 of the resistor pack to ground, thereby disabling these segments. Also, we’ve used a 10kΩ pull-up resistor to ensure that pins 3, 4, and 5 on the 74LS48 are in their inactive states (we will consider the functioning of these pins next month). 51 Main breadboard Logic analyzer breadboard Listing 3a: Our pin declarations for testing. 74LS48 B C A D D C B A 5 4 3 2 Fig.14: Connecting our LED-based logic analyser to the 74LS48 IC. your host computer to your Arduino. Don’t worry if your 7-segment displays are glowing dimly or showing spurious values. This is because we have not yet connected the outputs from the SN74LS48 to the ‘inputs’ of the current-limiting resistors. As we previously discussed (PE, August 2024), use your digital multimeter to ensure we have 5V (or thereabouts) between pin 8 and pin 16 on the IC (apply the multimeter’s probes directly to the IC’s pins). Next, leave the black probe on pin 8 and use the red probe to ensure we see the same 5V (give-or-take) value on pins 3, 4, and 5. So far, so good. Remove the USB cable to power everything down again, then reconnect the breadboard ends of the wires from pins 2, 3, 4, and 5 on the Arduino as illustrated in Fig.13(b). Observe that, the way we’ve wired things, inputs A, B, C, D on the 74LS48 (pins 7, 1, 2 and 6, respectively) are connected to pins 2, 5, 4, 3 on the Arduino, respectively. Don’t panic. I know we haven’t connected the outputs from the BCD decoder yet. For the moment, we are going to focus on its inputs. Wrapping one’s brain around all of this (which pins correspond to which signals and wires) can require some mental gymnastics. So, before we do anything else, we need to make sure we know what we’re doing and that we are controlling things the way we want to control them. To help with this, we’re going to use four of the probes on the logic analyser board we constructed earlier (PE, August 2024), as illustrated in Fig.14. Don’t forget to connect the logic analyser’s upper power and ground rails to their counterparts on the main breadboard. Before we power everything up, let’s 52 first create a small test program to make sure we are talking to the BCD decoder in a language it understands (file “CBOct24-03.txt”). As usual, we won’t go through everything here – we’ll just hit the highlights. As you’ll see when you look at the code, we are using variables of type int (integer) to represent our BCD values. Integers are stored as 16-bit values in the Arduino Uno, but we will be using only the four least-significant bits to represent values 0 through 9 in decimal (0000 through 1001 in binary). As part of this, we define pins driving our BCD decoder are outputs and set them LOW also. Last, but not least, we assign a value of 0 to our ValBcd variable. The main part of our test program is shown in Listing 3b. Let’s start with the new function called DisplayBcd(), into which we pass the BCD value we wish to display. This works similarly to the DisplaySegs() function we’ve been using to drive our displays directly. We described this in detail in PE, April 2023. All we need to note here is that our new function will present bits 0, 1, 2, and 3 of our BCD value to Arduino pins 2, 5, 4, and 3, respectively. Finally, we have the loop() function, which is as simple as simple can be. It starts on Line 40 by calling our new DisplayBcd() function to display the current value stored in ValBcd. On Line 41, we pause for ON_TIME, which we’ve set to one second. On Line 42, we increment the value stored in ValBcd. The use of the modulus/ integer remainder (%) operator means our count will follow the sequence 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and back to 0 again. OK, let’s power up our Arduino and then load and run our test program. Changing each second, our logic analyser LEDs should reflect the binary NUM_BCD_BITS to be 4. We declare a global integer variable called V a l B c d (think “BCD value”). We also declare an array of integers called PinsBcd[] to store the numbers of the Arduino pins we wish to use to drive our BCD decoder. This declaration is illustrated in Listing 3a. In the setup() function, we specify that the pins driving our 2:4 decoder are outputs and we set them both to LOW, thereby selecting display D0 (which we will be using a little later). Next, we specify that the Listing 3b: The body of our test program. Practical Electronics | October | 2024 Inputs to BCD Components from Part 1 0 LEDs (assorted colours) Resistors (assorted values) Solderless breadboard Multicore jumper wires (male-to-male) 1 Components from Part 2 2 7-segment display(s) ValBcd D C B A 3 Momentary pushbutton switches Components from Part 6 5 Passive piezoelectric buzzer 6 Components for Part 9 Components for Part 10 8 Breadboard mounting trimpots 9 Components for Part 12 https://amzn.to/3KmxjcX https://bit.ly/46SfDA4 https://bit.ly/3QAuz04 Light-Dependent Resistor Fig.15: The expected logic analyser display. Components for Part 13 counting sequence depicted in Fig.15. If not, return to the instructions above and recheck the wiring. Once you have this working, power everything down, then add the wires connecting the outputs from the BCD decoder to the inputs of the currentlimiting resistors, as illustrated in Fig.12(b). As usual, you can download a PDF showing our new BCD-based breadboard setup in its entirety (file “CB-Oct24-04. pdf”). When you return power to the Arduino, you should see the values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0… appear on display D0. Components for Part 14 Practical Electronics | October | 2024 https://amzn.to/3Tk7Q87 SW-18010P vibration switch 7 Finally, it’s time to bring everything together. We’re going to take our old nonBCD clock program (file “CB-Oct24-02. txt”) and the BCD test program we just created (file “CB-Oct24-03.txt”), and “munge” them together to create a new BCD-based clock program. Why don’t you do this yourself to make sure you are totally on top of things? If you run into any problems, you can compare your solution to mine (file “CB-Oct24-05.txt”). OMG, it works! (I mean, I never doubted us for a minute...) You may notice that the 7-segment displays do not appear as bright as they used to be. There’s a reason for this, which is that they’re not as bright as they used to be. Previously, we were using 150Ω current-limiting resistors to drive the displays with 20mA. Since we were multiplexing four displays, each display was on for only 25% of the time. That meant each display used to receive 20mA for 25% of the time and 0mA for 75% of the time, averaging out at 5mA per display. https://amzn.to/3Afm8yu Components from Part 5 4 All together now! https://amzn.to/3E7VAQE https://amzn.to/3O4RvBt https://amzn.to/3O2L3e8 https://amzn.to/3O4hnxk https://bit.ly/3S2430m BC337 NPN Transistor https://bit.ly/40xAgyS HC-SR04 Ultrasonic Sensor https://bit.ly/49AMBq4 Components for Part 15 Real-Time Clock (RTC) https://bit.ly/3S9OjHl Components for Part 18 Long tailed (0.1-inch/2.54mm pitch) header pins https://bit.ly/3U1Vp2z Components for Part 19 Prototyping boards Kit of popular SN74LS00 chips https://bit.ly/3UMkcZ1 https://bit.ly/3wqgzyv Components for Part 20 16V 100µF electrolytic capacitors Ceramic capacitors (assorted values) https://bit.ly/44LzpNa https://bit.ly/4bEAUiv Components for Part 22 SN74LS48N BCD Decoders 16-pin resistor pack (8 × 390Ω) Now, due to our 74LS48 BCD decoder’s outputs being limited to only 6mA, we’ve changed our current-limiting resistors to 390Ω, so each display is seeing an average of only 1.5mA, which explains why they appear dimmer now. Blowing one’s own flügelhorn Modesty forbids me from being boastful. Happily, members of the PE community are usually pleased to oblige. For example, I just received an email from a reader we will call Ian (because that’s his name). He wrote: Dear Max, I have to get this boast in while acknowledging that I’ve obviously learned lots from you over the last year and a half. Some time ago, I bought a set of 4-digit, 7-segment displays from AliExpress. The problem was the unit is common anode. I am quite proud of myself as I was able to work out which transistors to use. Also, which resistors for both the LEDs and the transistor base. I’m https://bit.ly/3zT18jx https://bit.ly/4d0ISDz happy to report that it worked first time (that’s a first)! It was the “I’ve obviously learned lots from you over the last year and a half” portion of this message that caught my eye. My mother will be so proud. We always suspected that someone other than her was reading these columns. Now we know his name! Next time In our next column, we will dive deeper into the functioning of the 74LS48 decoder. After that, we will introduce a different BCD decoder integrated circuit that will better serve our needs, including addressing our lack-of-brightness issue. Until that frabjous day, if you have any thoughts you’d care to share, as always, I welcome your insightful comments, penetrating questions, and sagacious PE suggestions. 53