# Binary Numbers Explained

Here’s a really quick guide to binary numbers, because I use them in other posts and haven’t fully explained myself.

OK. Binary numbers are represented using only 1s and 0s:

01101001

This is the number 105 in binary. Honest.

How does that work then?

Binary works because it relies on a ‘power of two’ system. What this means in practice is that each digit (which is either a 1 or a 0), represents a power of two value. A power of two value is the number 2, raised to a numerical power, from 0 – n.

This sounds weirder than it actually is.

Here are the first eight power of two values:

2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128

If you want to delve into the mathematics behind this, good on you. If that makes your head hurt and binary numbers are more than enough thank you, then read on.

In binary, powers of two are represented from right to left, in ascending order. Note that the power of two value is always double the previous one:

128 | 64 | 32 | 16 |  8 |  4 |  2 |  1

And when you specify a 0 or 1, you’re basically saying if this number exists in your number.

128 | 64 | 32 | 16 |  8 |  4 |  2 |  1
0 |  1 |  1 |  0 |  1 |  0 |  0 |  1

So we have 64 + 32 + 8 + 1 = 105.

So a number in binary is represented by ‘ticking’ the box of the relevant power of two value.

When I use binary numbers, this is what’s going on.

So:

01000011 = 67   (64+2+1)
11110011 = 243  (128+64+32+16+2+1)
00001001 = 9    (8+1)

Simple 🙂

### 6 thoughts on “Binary Numbers Explained”

1. Binary numbers, nice!

But, why have you not tackle the part after the coma.
You know, whole numbers and after…

• I’m not sure what you mean by “the part after the coma”?

2. Is the avatar optional?

Please could I have different than that: r=e^{\sin \theta} – 2 \cos (4 \theta ) + \sin^5\left(\frac{2 \theta – \pi}{24}\right)

thing it might be miss leading.