Number Systems | Conversions
Number systems are used in computer programming and other forms of digital communication. The most common system is the Decimal Number System, which includes the digits 0 to 9...
DECIMAL (base10) = 10 digits
00 01 02 03 04 05 06 07 08 09
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
As an example, the number 369 is represented as...
369 = three hundreds (3*100), six tens (6*10), and nine ones (9*1)
or...
369 = 3*10^2 (300) + 6*10^1(60) + 9*10^0 (9)
^ the power of
* multiplication
The Binary Number System has two digits, 0 and 1. The 0 represents false (off) and the 1 represents true (on). In binary, 100 is read as one zero zero...
BINARY (base2) = 2 digits
0 bit = false
1 bit = true
A bit is a binary digit
A byte is 8 bits
Power of 2's (right to left) ...1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1
Any decimal number can be converted into a binary number. The following table shows the binary translation of a decimal number. Each placeholder in the binary number represents a power of 2...
0 0 0 0 = 0
0 0 0 1 = 1
0 0 1 0 = 2
0 0 1 1 = 3
0 1 0 0 = 4
0 1 0 1 = 5
0 1 1 0 = 6
0 1 1 1 = 7
1 0 0 0 = 8
1 0 0 1 = 9
1 0 1 0 = 10
___________
8,4,2,1 Power of 2's (right to left)
The Octal Number System includes the digits from 0 to 7...
OCTAL (base8) = 8 digits
00 01 02 03 04 05 06 07
10 11 12 13 14 15 16 17
20 21 22 23 24 25 26 27
30 31 32 33 34 35 36 37
Each digit in an octal number represents three bits.
Power of 8's (right to left) ...32768, 4096, 512, 64, 8, 1
The Hexadecimal Number System includes the digits from 0 to 16. The numbers 10 to 15 are representd as letters from A to F...
HEXADECIMAL (base16) = 16 digits
00 01 02 03 04 05 06 07 08 09 A B C D E F
10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F
20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F
30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F
Each digit in an hexadecimal number represents four bits.
Power of 16's (right to left) ...65536, 4096, 256, 16, 1
| Dec | Bin | Oct | Hex |
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
