DeepakBhalla

Converting Binary to Decimal in your head

By Deepak Bhalla Sun 30 July 2017 1 min read

It's actually relatively easy to convert from binary to decimal in your head. Memorising a small but manageable lookup table allows you to spot patterns in binary numbers.

000     0
001     1
010     2
011     3
100     4
101     5
110     6
111     7

From there all you need to realise is that shifting the lookup table value to the left once multiplies the value by two:

00001110 = (7 * (2^1)) = 14

Using the lookup table we can see the pattern 111 (which in the lookup table corresponds to 7) which is shifted up by one place (2 ^ 1) which gives the decimal value of 14.

Processing more complicated numbers is easy:

00011000 = 3 * (2^3) = 24

Using the lookup table we can identify the pattern 011 (which in the lookup table corresponds to 3) which we shift up 3 positions (2 ^ 3) which gives us the total value 24. This can also be done by identifying 110 (corresponds to 6) shifted up (2 ^ 2) which is also 24.

We also don't have to shift:

01010111 = (5 * (2^4)) + 7 = 87

Here we find two patterns 101 and 111. We shift 101 (5) up by 4 positions and keep 111 (7) where it is. The addition of the two gives the total decimal value.

01111001 = ((7 * (2^4)) + (4 * (2^1)) + 1) = 121
Deepak Bhalla