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

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

Author

Christina Sng is a three-time Bram Stoker Award-winning author that finds peace in mathematics and the macabre. Her poetry, fiction, essays, and art appear in Fantastic Stories of the Imagination, Interstellar Flight Magazine, and The Washington Post. Aside from having over 20 years of experience in the field of writing, she also has an extensive background in UX design and IT. Her educational background combined with her interests and neverending curiosity about the world is the perfect recipe to have her tackle fascinating topics about math. She is able to approach the highly logical field of mathematics through an extremely creative lens that sheds new light and exposes new avenues on how it impacts our lives.