Make Electronics

Chips, Ahoy! 185

Experiment 19: Learning Logic

BAckground

From Boole to Shannon (continued)

Ann is

wearing

the hat

Bob is

wearing

the hat

This

combination

can be

YES

YES

YES

NO

NO NO

YES

NO

TRUE

TRUE

FALSE

TRUE

Figure 4-52. The hat-wearing possibilities can be expressed in a
“truth table.”

Input A Input B Output

21

21

21

2))

2)) 2))

21

2))

21

21

2))

21

Figure 4-53. The truth-table from can be relabeled to describe
the inputs and outputs of a NAND gate.

A very simple telephone problem could be expressed like

this. Suppose two customers in a rural area share one tele-

phone line. If one of them wants to use the line, or the other

wants to use it, or neither of them wants to use it, there’s

no problem. But they cannot both use it at once. You may

notice that this is exactly the same as the hat-wearing situa-

tion for Ann and Bob.

We can easily draw a circuit using two normally closed

relays that creates the desired outcome (see Figure 4-54),

but if you imagine a telephone exchange serving many

thousands of customers, the situation becomes very compli-

cated indeed. In fact, in Shannon’s time, no logical process

existed to find the best solution and verify that it used fewer

components than some other solution.

Shannon saw that Boolean analysis could be used for this

purpose. Also, if you used an “on” condition to represent

numeral 1 and an “off” condition to represent numeral 0,

you could build a system of relays that could count. And if it

could count, it could do arithmetic.

When vacuum tubes were substituted for relays, the first

practical digital computers were built. Transistors took the

place of vacuum tubes, and integrated circuit chips replaced

transistors, leading to the desktop computers that we now

take for granted today. But deep down, at the lowest levels

of these incredibly complex devices, they still use the laws

of logic discovered by George Boole. Today, when you use

a search engine online, if you use the words AND and OR to

refine your search, you’re actually using Boolean operators.

Output

Input A Input B

Figure 4-54. This relay circuit could illustrate the desired logic for two telephone customers wanting to share one line, and its
behavior is almost identical to that of the NAND schematic shown in Figure 4-48.