Section 2.3

Section 2.3
Octal Number System

The octal number system has a base of eight, meaning that it has eight possible digits: 0,1,2,3,4,5,6,7.

8³ 8² 8¹ 8⁰ 8^-1 8^-2 8^-3

=512 =64 =8 =1 . =1/8 =1/64 =1/512

Most Significant Digit Octal point Least Significant Digit

Octal to Decimal Conversion

eg. 24.6₈ = 2 x (8¹) + 4 x (8⁰) + 6 x (8^-1) = 20.75₁₀

Binary-To-Octal / Octal-To-Binary Conversion

Octal Digit 0 1 2 3 4 5 6 7

Binary Equivalent 000 001 010 011 100 101 110 111

Each Octal digit is represented by three bits of binary digit.

eg. 100 111 010₂ = (100) (111) (010)₂ = 4 7 2₈

Repeat Division
This method uses repeated division by 8. Eg. convert 177₁₀ to octal and binary:

177/8 = 22+ remainder of 1 1 (Least Significant Bit)

22/ 8 = 2 + remainder of 6 6

2 / 8 = 0 + remainder of 2 2 (Most Significant Bit)

Result 177₁₀= 261₈

Convert to Binary = 010110001₂

8³	8²	8¹	8⁰		8^-1	8^-2	8^-3
=512	=64	=8	=1	.	=1/8	=1/64	=1/512
Most Significant Digit				Octal point			Least Significant Digit

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

`177/8`	`= 22+ remainder of` `1`	`1 (Least Significant Bit)`
`22/ 8`	`= 2 + remainder of` `6`	`6`
`2 / 8`	`= 0 + remainder of` `2`	`2 (Most Significant Bit)`
`Result`	`177`₁₀`=`	`2``6``1`₈
	`Convert to Binary`	`= 010110001`₂