## Math and Computers

Christina Sng for Maths@Singapore

Math opened up an incredible world for computing. By having a computer help us count, we can make calculations of very large numbers.

How does a computer help us accomplish this?

**Binary**

Computers convert every number into a binary and express it in base 10. For example:

Every 10 ones = 1 ten

Every 10 tens = 1 hundred

With a binary, you go up a unit every 2 numbers:

2 ones = 1 two

2 twos = 1 four

This means the number 9 is 1001 in binary:

1 one, 0 twos, 0 fours, and 1 eight

or

1 + 8 =9

Computers use binaries because it is easier to build circuits with values of 1 or 0 than circuits with 10 separate values.

**Addition**

Adding in binaries to addition on a computer is straightforward:

If you have 2 numbers with a 1 value, you store a 0 and move carry 1. If not, you keep the bigger of the two numbers in that slot.

In an example:

5 + 4 = 0101 + 0100

In the first slot, you have a 1 + 0, therefore you record the bigger number, 1.

The second slot contains two 0s, so you record 0 (since both numbers are the same.

In the third slot with two 1s, you record a 0 and carry a 1.

What remains is 1001, or 9.

**Multiplication**

Computers use long multiplication in binary. So if a computer multiplies a number by 1, it returns a 1, a much simpler system than base 10 despite requiring more steps.

As illustrated in this example:

In base 10, 8 x 9 is easy to solve with no long multiplication.

In binary, each number is 4 digits long, resulting in a solution 7 digits long.

**Subtraction**

In computing, subtraction is a little more complicated. It is conducted in two steps:

A binary computer adds its compliment, a number with ones where the original has zeros, and zeros where the original has ones.

Here’s an example to help:

4 = 0100 in binary

-4 = 1011

Therefore, 7 – 4 = 0111 + 1011 = 10010.

The leftmost number is subsequently moved to the right, resulting in 0011 = 3.

Excited to find out more? Visit https://sciencing.com/convert-between-base-number-systems-8442032.html

Thanks to Clément Hélardot @clemhlrdt for making this photo available freely on Unsplash