How does a calculator work things out?

Question

If I wanted to know how many 9's there are in say 72 for example (assuming I had no knowledge of the 9 times table) I could arrive at the total using three basic methods - two of which are in the written form. You have basic division and you also have long division. The third method is mental arithmetic. Although there are possibly more since not every person will arrive at the answer using the same mental route.

However a calculator can neither think nor write. It's only method of 'reasoning' is arithmetic logic. But how do you go about working out 72 divided by 9 just by using digital logic?

There is a method for doing long division but what is the method for calculating my example using logic? Please show how you arrive at 8 using logic to calculate 72/9.

So far all of the answers provided tell me that most of you don't actually know 'how' calculators/or any device containing a microprocessor work.

I'm not asking for the components of logic such as AND, NOT & OR. Nor am I asking how they are powered. I just want to know how calculators derive at any given answer using logic.

A step-by-step example of how a calculator would arrive at 8 when 72 is divided by 9 would be a bonus.

Thank you.

Answer 1

The same as any computer, using binary arithmetic and Boolean logic. It's actually interesting to see how it's done. Anything a computer does comes down to three Boolean operations: AND, OR and NOT. between zeros and ones.

Answer 2

You must provide the computer with 'input' for example 72 / 9 and hit 'operate' = to activate the computer. The computer is 'programed' to recognize the sequenced input 72 and 9 and the 'operator' (divide) and that all input is complete (hit =). The program then performs a series of very simple calculations but at lightning speed and absolute accuracy. The numbers 72 and 9 are transformed into binary code (0's and 1's) which must be added or subtracted (but not multiplied or divided). For example, the computer could subtract 9 from 72 until the remainder is zero or a value less than 9 and provide as output the number of times the subtraction occurred (8) and the remainder (in decimal) if any. The operation sign (divide) triggers Boolean logic circuits to supervise the calculation and translate the result from binary code to a numeric answer. Google "How Stuff Works" to learn more about the workings of a PC and Boolean logic. The devil is in the details. Good luck.

Answer 3

A calculator uses logic gates such as AND, OR, and NOT. Actually it uses more exotic gates like NAND and XOR more frequently, but these can be defined in terms of those above: NAND (x, y) = NOT (AND (x,y)), XOR (x, y) = AND (OR (x, y), NAND (x, y)).

These individual logic gates are actually represented as small bits of metal on the silicon chips, with 'wires' painted on the boards connecting them.

The first step in dividing the numbers is to calculate the value of each digit and convert it to the correct format for internal use. This is fairly boring, so I'll omit it. Suffice it to say that when you see the first "7" a calculator might see 0111 instead (the first wire has no current and the other three carry currant).

The division is normalized, so that each number is treated as a.bcdef. In your case, this is 7.200000 divided by 9.000000, with a note on the wire to add one carry place. Boolean-wise, the number of digits in the first number is stored in the same format as the numbers, with a "bias" (the leading 1) that also allows for negative numbers (in the exponent, representing numbers close to 0, like 7.1E-10). This example might use exponent fields of 10001 and 10000, representing E+01 and E+00, respectively. (01111 would represent E-01, in that case.) The two are subtracted in the following way; this simplified example uses w.x as the number larger in magnitude and y.z as the other:

First digit: AND (NOT (y), AND (w, NAND (x, z)))
Last digit: XOR (x, z)

The division itself is done with similar boolean logic, generally using a lookup table.

Answer 4

On the first modern calculator, they progamed every sibgle sum ever on it and then it was copied on to the rest of the calculators. In brief, it's all to do with a chip. Not a chocolate chup, a computer chip (lol). It's realyy complicated and all the simbols I need to explain it thouroughly are not even on the key board!!!

Hope I helped

Answer 5

Binary. I forgot how it's done but I think you take the inversion of the the divisor or something or was that subtraction. I don't remember. I don't care. I know my 9 times multiplication table.

Answer 6

I think it works the same as a computer using binary numbers
They use different sums to make the machine do different things im not sure if this is right but there you go:D

Answer 7

tiny little Japanese geniuses bred in a special lab and placed inside at the factory..... They sneak out at night to get food and water etc....

Answer 8

in binary

Answer 9

it's called a solar panel