Binary

What is binary?

Binary is the language of computers. It’s a base-2 counting system - meaning that it only uses 2 numbers, a 1 and a 0 whereas we use (usually) use a base-10 counting system consisting of numbers 0 to 9.

This is because it is easier and more efficient when all communication is literally done through signals sent by electricity.

How to count in binary?

Counting is the same in binary as it is in decimal. The only difference is that each digit represents more numerical value than decimals.

For example,

$$\begin{array}{rl}35& =30+5\\ 154& =100+50+4.\\ 3593& =3000+500+90+3.\end{array}$$

The pattern is the higher the digit, the higher the power of 10 (hence base-10).

$$\begin{array}{rl}35& =(3\ast 10^1)+(5\ast 10^0)\\ 154& =(1\ast 10^2)+(5\ast 10^1)+(4\ast 10^0)\\ 3593& =(3\ast 10^3)+(5\ast 10^2)+(9\ast 10^1)+(3\ast 10^0)\end{array}$$

Binary counting is exactly the same, with each digit being a power of 2, and the value is either there or not there.

$$\begin{array}{rl}35& =32+2+1\end{array}$$

Notice how all values above are powers of 2.

Expanded, it’ll look like so:

$$35=(1\ast 2^5)+(0\ast 2^4)+(0\ast 2^3)+(0\ast 2^2)+(1\ast 2^1)+(1\ast 2^0)$$

or in binary form:

$$35=100011$$

Converting from binary to decimal

Converting from decimal to binary