Counting in Binary

Binary (base-two) numbers are only made of 0s and 1s. Counting in binary is similar to counting decimal (base-ten) numbers, that is one of the most popular numeral systems.

Counting in Binary
Black background with 0s and 1s forming a square

Binary (base-two) numbers are only made of 0s and 1s. Counting in binary is similar to counting decimal (base-ten) numbers, that is one of the most popular numeral systems. Let's explore these two systems:

Decimal

Instruction Result
Start at 0 0
Count 1, 2, 3, 4, 5, 6, 7, 8, 9 9
Turn the 9 into a 0 adding 1 to the left 10
Count up to 99 99
Turn the 00 into 00 adding 1 to the left 100

In binary since it moves much quicker:

Instruction Result
Start at 0 0
Add 1 1
Turn 1 to 0 and add 1 to the left 10
Add 1 11
Turn 11 into 00 adding 1 to the left 100
Add 1 101
Turn 1 into 0 and add 1 to the left 110
Add 1 111
Turn 111 to 000 and add 1 to the left 1000
Add 1 1001

The ASCII (American Standard Code for Information Interchange) character code chart demonstrates the equivalency between these two systems, using an 8-bit system:

Decimal Binary
0 00000000
1 00000001
2 00000010
3 00000011
4 00000100
5 00000101
6 00000110
7 00000111
8 00001000
9 00001001
10 00001010
11 00001011
12 00001100
13 00001101
14 00001110
15 00001111
16 00010000
17 00010001
18 00010010
19 00010011
20 00010100
21 00010101
22 00010110
23 00010111
24 00011000
25 00011001
26 00011010
27 00011011
28 00011100
29 00011101
30 00011110
31 00011111

Every time we add a 1 to the left, the number gets doubled. Using a binary number of 10011011 as an example, if we break it down it gives us the following:

Digit Multiplier
1 128
0 64
0 32
1 16
1 8
0 4
1 2
1 1

If we multiply each digit by its multiplier, we get 155.

If you use all the rules you have learned in this note, you can count binary up to 31 with one of your hands. With both hands you count up to 1,023. This is useful if you are trying to count big numbers and don't have a pen, paper or any device with a calculator. The following video shows how to count up to 31 in binary using your hands:

This note was inspired by a project I worked on called Binary Clock, where I use binary to count time.


References