How Calculators Work

How a Calculator Calculates

As you learned on previous pages, most calculators depend on integrated circuits, commonly known as chips. These circuits use transistors to add and subtract, as well as to perform computations on logarithms in order to accomplish multiplication, division and more complicated operations such as using exponents and finding square roots. Basically, the more transistors an integrated circuit has, the more advanced its functions may be. Most standard pocket calculators have identical, or very similar, integrated circuitry.

Like any electronic device, the chips inside a calculator work by reducing any information you give it to its binary equivalent. Binary numbers translate our numbers in a base-two system, in which we represent each digit by a 1 or a 0, doubling each time we move up a digit. By "turning on" each of the positions -- in other words, by putting a 1 in it -- we can say that that digit is included in our overall number.

Microchips use binary logic by turning transistors on and off literally, with electricity. So, for example, if you wanted to add 2 + 2, your calculator would convert each "2" to binary (which looks like this: 10) and then add them together. Adding the "ones" column (the two 0s), gives you 0: The chip can see that there is nothing in the first position. When it adds the digits in the "tens" column, the chip gets 1+1. It sees that both are positive, and -- since there are no 2's in binary notation -- moves the positive reply one digit to the left, getting a sum of 100 -- which, in binary terms, equals 4 [source: Wright].

This sum is routed through the input/output chip in our integrated circuit, which applies the same logic to the display itself. Have you ever noticed the way the numbers on a calculator or alarm clock are made up of segmented lines? Each one of those parts of the numerals can be turned on or off using this same binary logic. So, the processor takes that "100" and translates it by lighting up or turning on certain segments of the lines in the display to create the numeral 4.

On the next page, we'll look at the calculator's impact on the world and how we can expect to see them develop in the future.