### 4. Octal and Hexadecimal number system

posted Jun 30, 2014, 9:50 PM by Maurice Nyamoti   [ updated Jan 11, 2016, 9:33 PM ]

## Octal Number System

• Octal number system uses eight digits running from 0-7 to represents values of a number. the place value go up in a factor of 8
Example:

The table below clearly shows how octal numbers grow with a factor of 8 from left to right

 Place Values (8n) Eights 83=512 Fours 82=64 Twos 81=8 Ones 80 =1 Octal Digit 6 5 0 2

• This number system has a radix of 16. It uses sixteen digits ranging from 0-9 and letters A-F where A is equivalent to 10, up to F which is equivalent to 16.
• The place value of hexadecimal numbers goes up in factors of sixteen as shown in the table below:

The table below clearly shows how hexadecimal numbers grow with a factor of 16 from left to right

 Place Values (16n) 163= 4096 162=256 161=16 160 =1 Hexadecimal Digit 7 8 3 3

### Reasons for using octal and hexadecimal number systems

1. A single octal or hexadecimal digit encodes more than one binary digit. This is automatic data compression, hence storage mediums can save on space
2. Instead of transmitting long digits of '0's and '1's between devices, the data can be encoded as octal or hexadecimal to improve transmission efficiency.

### Numeral systems conversion table

Decimal

Base-10

Binary

Base-2

Octal

Base-8

Base-16

0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 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
16 10000 20 10
17 10001 21 11
18 10010 22 12
19 10011 23 13
20 10100 24 14
21 10101 25 15
22 10110 26 16
23 10111 27 17
24 11000 30 18
25 11001 31 19
26 11010 32 1A
27 11011 33 1B
28 11100 34 1C
29 11101 35 1D
30 11110 36 1E
31 11111 37 1F
32 100000 40 20

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