4.5.2.1 Number Base

Humans and computers are incompatible when they try to count. While Humans use Decimal and Unary systems of counting, computers can only interpret Binary. This is because computers can only process the presense or an absense of a signal, on or off, 1 or 0.

Characters

When writing down numbers, humans (while using base 10) have a choice of ten characters. Computers only have a choice of two characters.

Below is a selection of different base systems and their characters.

Number System Available Characters
Decimal (base 10) 0 1 2 3 4 5 6 7 8 9
Unary (base 1) 1
Binary (base 2) 0 1
Octal (base 8) 0 1 2 3 4 5 6 7
Hexadecimal (base 16) 0 1 2 3 4 5 6 7 8 9 A B C D E F

Conversions

Dec Bin Oct Hex Unary
0 0 0 0
1 1 1 1 1
2 10 2 2 11
3 11 3 3 111
4 100 4 4 1111
5 101 5 5 11111
6 110 6 6 111111
7 101 7 7 1111111
8 1000 10 8 11111111
9 1001 11 9 111111111
10 1010 12 A 1111111111
11 1011 13 B 11111111111
12 1100 14 C 111111111111
13 1101 15 D 1111111111111
14 1110 16 E 11111111111111
15 1111 17 F 111111111111111
16 10000 20 10 1111111111111111

To easily convert Decimal to Binary, attempt this methodology

Position \(2^7\) \(2^6\) \(2^5\) \(2^4\) \(2^3\) \(2^2\) \(2^1\) \(2^0\)
Decimal 128 64 32 16 8 4 2 1
12 No No No No Yes Yes No No

Convert simply by subtracting powers of two until they fit.

Converting binary to hexadecimal is equally as easy. Split the binary into groups of four and convert each 4 bits into a hex digit.