Binary

Addition

Introduction

Binary is a way of writing numbers with only two possible values for each digit- 1 and 0. Using these numbers, it is possible to create denary (normal) numbers like 9 using a line of binary that looks like this: 00001001. The numbers in binary go up in powers of two from right to left, so the rightmost number in the line of eight binary digits is 1, the second from the right is 2, the third from the right is 4, the fourth from the right is 8, and so on.

All denary numbers can be represented in binary.To make the denary number 12 in binary, for instance, you would write: 00001100. This would be equivalent to 8 + 4, which equals 12. Binary is used a lot in computers, which I shall talk about later.

A Brief History of the Binary System

A similar system to binary was first mentioned hundreds of years ago in the 3rd century B.C by Indian mathematician Pingala. This coincided with the discovery of 0. The first modern use of binary was written down by a German mathematician, Gottfried Leibniz, in the 1600s. Leibniz used 1s and 0s like in the binary we use today. The real breakthrough was in November 1937, when George Stibitz made a computer that used binary for addition.

What is Binary Used For?

Binary is used mainly by computers nowadays. A computer functions by manipulating 1s and 0s. It could be said that binary is the language of the computer. As this is being typed, the computer is storing the letters I am typing as their binary equivalents, which are then converted back to the letter I typed and being displayed (printed) on my computer screen. This could not happen without binary. Without binary, we wouldn't be using computers the way we do.

Programming languages exist because without them programmers would have to use a complex and unfriendly mixture of 1s and 0s to write even the simplest programs. With programming languages, the code written gets converted to binary so the computer can understand it. It's a bit like someone speaking to someone who speaks a different language using a translator. One person says something to the translator in their language, who repeats it to the other person in their (different) language.

Binary Addition and Subtraction

In Binary, you can add and subtract numbers. The picture in the corner shows how. However, problems can sometimes occur with addition in binary if the amount of bits available for use is limited. For example, if you were adding:

11111110

and

11111111

together, it would come out something like this:

100000001


This is not allowed, because binary can only have 8 digits in it or less, NO MORE. When this happens, it is known as "Binary Overflow".