Make: Electronics by Charles Platt (classic books to read TXT) 📗

In binary we do the same thing, except that we restrict ourselves to digits 0 and 1 only. So begin with 0 in the rightmost position, and count up to 1. As 1 is our limit, to continue counting we carry 1 over to the next place on the left, and start again from 0 in the right-most position. Count up to 1, then add 1 to the next place on the left—but, it already has a 1 in it, so it can’t count any higher. So, carry 1 from there one space further, to the next place beside that—and so on.

If a glowing LED represents a 1, and a dark LED represents a 0, the diagram in Figure 4-105 shows how the 74LS92 counts up from 0 to (decimal) 5 or (binary) 101 in its inimitable fashion. I’ve also included a diagram in Figure 4-106 showing how a counter with four binary outputs would display decimal numbers from 0 through 15, again using the LEDs to represent 1s and 0s.

Figure 4-106. A hexadecimal (16-based) binary counter would generate this succession of high states from its four output pins as it counts from 0 through 15 in decimal notation.

Here’s a question for you: how many LEDs would you need to represent the decimal number 1024 in binary? And how many for 1023?

Obviously binary code is ideally suited to a machine full of logic components that either have a high or a low state. So it is that all digital computers use binary arithmetic (which they convert to decimal, just to please us).

Getting back to our project: I want to take the three binary outputs and make them create patterns like the spots on a die. How can I do this? Quite easily, as it turns out.

I’m assuming that I’ll use seven LEDs to simulate the patterns of spots on a die. These patterns can be broken down into groups, which I have assigned to the three outputs from the counter in Figure 4-108. The first output (farthest to the right) can drive an LED representing the dot at the center of the die face. The second (middle) output can drive two more diagonal LEDs. The third output must switch on all four corner LEDs.

This will work for patterns 1 through 5, but won’t display the die pattern for a 6. Suppose I tap into all three outputs from the counter with a three-input NOR gate. It has an output that goes high only when all three of its inputs are low, so it will only give a high output when the counter is beginning with all-low outputs. I can take advantage of this to make a 6 pattern.

Note that it’s bad practice to mix the LS generation of TTL chips with the HC generation of CMOS chips, as their input and output ranges are different; so, the NOR chip has to be a 74LS27, not a 74HC27.

We’re ready now for a simple schematic. In Figure 4-107 I’ve colored some of the wires just to make it easier for you to distinguish them. The colors have no other significance.

Figure 4-107. A simplified schematic shows how outputs from the 74LS92 counter can be combined, with signal diodes and a single three-input NOR gate, to generate the spot patterns on a die. The wire colors have no special meaning and are used just to distinguish them from each other.

Figure 4-108. Binary outputs from the 74LS92 counter can be used to power LEDs arrayed in groups to simulate the pattern of spots on a die.

Each of the LEDs is grounded through a separate 4K7 load resistor. Unfortunately, this means that when they are displaying the pattern for a 6, all of them are running in parallel from the output of the NOR gate, which overloads it. As long as you don’t leave the display in this mode for very long periods, it shouldn’t cause a problem. You could compensate by increasing the load resistors, or by running pairs of the LEDs through one resistor, but this will make them so dim that they’ll be difficult to see, as they’re so close to their lower limit for current already.

Notice how I have added four signal diodes, D1 through D4. When Output C goes high, it has to illuminate all four corner LEDs, and so its power goes into the brown wire as well as the gray wire. But we must never allow one output to feed back into another, so D4 is needed to protect Output B when Output C is high.

Because there is now a connection between B and C, we need D2 to protect Output C when Output B is high. And because Output B must only feed two of the corner LEDs, we also need D3 to stop it from illuminating the other two. And, we have to protect the output from the NOR gate when either Output C or Output B is high. This requires D1.

Figure 4-109 shows everything that I’ve described so far assembled in breadboard format, while Figure 4-110 shows the test version that I built. Note that the unused logical inputs on the 74LS27 chip are shorted together and connected to the positive side of the power supply. Here’s the rule:

When using CMOS chips (such as the HC series), connect unused logical inputs to the negative side of the power supply.

When using TTL chips (such as the LS series), connect unused logical inputs to the positive side of the power supply.

Figure 4-109. With some extra components, the schematics from Figures 4-102 and 4-107 can be combined to make the working dice simulation.

I assume that you have had enough fun watching the LEDs count slowly, so I’ve changed the capacitor and resistor values for the 555 to increase its speed from approximately 1 pulse per second to about 50,000 pulses per second. The counter could run much faster than this, but I just want