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→Victorian Precursor
"I know what you're thinking about," said Tweedledum: "but it isn't so, nohow." "Contrariwise." continued Tweedledee, "it if was so, it might be: and if it were so, it would be: but as it isn't, it ain't. That's logic."
'''— LB'''
=1100? That's 12, right?=
Perhaps you are young enough to have studied "new math."
Or old enough to have struggled with helping your kids with "new math." But if not, or if you need a bit of review since the days you thankfully put the math books behind you, when thinking of computers you must realize that the decimal system we find so natural is completely arbitrary.
Computers, being binary, not decimal, operate on a binary system.
In the binary system, 10 does not represent "ten," but two. The number written as "100" represents four. Three is 11, five is 101, seven is 111 and eight is 1000. If you are doing your budget in a ledger with a pencil, this is obviously an unhandy way to go about it, compared to the decimal system. And you don't type it into your computer that way either.
Instead, you type in, say, your $12 subscription to Home Computer Compendium. Each key of your computer that you touch sets off a series of switches, on and off. The 12 that you type is 1100 in the math your computer uses, but still shows up as 12 on the screen so that you can read it without adding in your head. And if you type in the dollar sign, that is coded in with a series of on-off combinations as well.
Whatever your computer is doing, it is doing is by addition.
In binary logic, possibilities are aligned by the basic logical operations. These operations are conjunction ("and"), disjunction ("or"), negation ("not"), implication ("if then") and bi-implication ("if and only if"). Each has a different "truth value" according to the truth of its components.
For instance, the sentence "Caroline and Stephanie are girls," is true, but the sentence "Caroline and Albert are girls" is false, assuming that Caroline and Stephanie are both girls and Albert is a boy.
However, "Caroline is a girl or Albert is a girl" would have the truth value of "true": so would "Caroline is a girl or Stephanie is a girl" because the "or" function here does not have the "either/or" implications it has in ordinary speech. "Caroline is a canary or Albert is an albatross" would however, be false.
So, depending on which logical function is being used, a circuit can be designed which can be on if Switch A and Switch B are both on, or if either were on. for instance. Or, the circuit can be programmed to come on only if Switch A is on, or Switch B is on, but not both. And so on.
The thousands of switches on each silicon chip are what makes the huge number of operations on your TI99/4A possible. The fact that so many switches can be placed in such a tiny space is also what makes it possible for you to have a computer in a corner of your house.
'''— LB'''
