The Way Micros Count

Unlike us, microprocessors have not grown up with the idea that 10 is a convenient number of digits to use. We have taken it so much for granted that we have even used the word digit to mean both a finger and a number. Microprocessors and other digital circuits use only two digits – 0 and 1 – but why? Ideally, we would like our microprocessors to do everything at infinite speed and never make a mistake. 

Error free or high speed – which would you feel is the more important? It’s your choice but I would go for error free every time, particularly when driving my car with its engine management computer or when coming in to land in a fly-by-wire aircraft. I think most people would agree.
So let’s start by having a look at one effect of persuading microprocessors to count in our way.I f the input of a microprocessor is held at a constant voltage, say 4V, this would appear as in Figure

If we try to do this in practice, then careful measurements would show that the voltage is not of constant value but is continuously wandering above and below the mean level. These random fluctuations are called electrical noise and degrade the performance of every electronic circuit. We can take steps to reduce the effects but preventing it altogether is, so far, totally impossible. We can see the effect by disconnecting the antenna of our television. The noise causes random speckles on the screen which we call snow. The same effect causes an

audible hiss from the loudspeaker. The effect of noise is shown in Figure

Most microprocessors use a power supply of 5 V or 3.3V. To keep the arithmetic easy, we will assume a 5 V system. If we are going to persuade the microprocessor to count from 0 to 9, as we do, using voltages available on a 5 V supply would give 0.5V per digit:

0 = 0V

1 = 0.5V

2 = 1V

3 = 1.5V

4 = 2V

5 = 2.5V

6 = 3V

7 = 3.5V

8 = 4V

9 = 4.5V

If we were to instruct our microprocessor to perform the task 4 + 4 = 8, by pressing the ‘4’ key we could generate a 2 V signal which is then remembered by the microprocessor. The + key would tell it to add and pressing the ‘4’ key again would then generate another 2V signal. So, inside the microprocessor we would see it add the 2 V and then another 2 V and, hence, get a total of 4V. The microprocessor could then use the list shown to convert the total voltage to the required numerical result of 8. This simple addition is shown in Figure 2.3. This seemed to work nicely – but we ignored the effect of noise. Figure 2.4 shows what could happen. The exact voltage memorized by the microprocessor would be a matter of chance. The first time we pressed key 4, the voltage just happened to be at 1.5 V but the second time we were luckier and the voltage was at the correct value of 2V.
Inside the microprocessor:
1.5 V + 2V = 3.5V
and using the table, the 3.5 V is then converted to the number 7. So our microprocessor reckons that 4 + 4 = 7.5! Since the noise is random, it is possible, of course, to get a final result that is too low, too high or even correct.

sourced by: Introduction to Microcomputers and Microcontrollers by John Crisp