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Computer Systems. Dk Izzati Pg Haji Ahmad. Octal The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Each octal digit represents three binary digits. Conversion of binary to octal

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computer systems

Computer Systems

DkIzzati Pg Haji Ahmad

slide2

Octal

  • The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.
  • Each octal digit represents three binary digits
slide3

Conversion of binary to octal

  • Given a binary number, in order to convert it to an octal number, first of all, split the binary number into groups of 3 bits starting from the right.

Example: 110111001₂

110 111 001

6 7 1

Hence, 110111001₂ = 671₈

slide4

Conversion of octal to binary

  • To convert octal to binary, replace each octal digit by its binary representation.

Example:

Convert 518 to binary:

  • 58 = 1012
  • 18 = 0012
  • Thus: 518 = 101 0012
slide5

Conversion of octalto decimal

  • To convert a number k to decimal, use the formula that defines its base-8 representation:
  • In this formula, ai is an individual octal digit being converted, where i is the number of the digit (counting from 0 for the right-most digit).

Example:

Convert 7648 to decimal:

7648= 7 x 8² + 6 x 8¹ + 4 x 8° = 448 + 48 + 4 = 50010

slide6

Exercise

1. Convert the following binary numbers to octal

a. 101

b. 1001

c. 110101

d. 1110010

e. 11101011

f. 1110001101

g. 0001110100011

h. 111000011010101

slide7

2. Convert the following octal numbers to binary:

  • 65
  • 876
  • 2190
  • 67788
  • 324671
  • 4440134
  • 870145
  • 2506779
slide8

3. Convert the following octal numbers to decimal:

a. 90

b. 255

c. 2787

d. 44567

e. 2908043

f. 289001

g. 112009

h. 567830

slide10

Convert the following octal numbers to hexadecimal:

  • 79
  • 321
  • 673
  • 2098
  • 123025
  • 401099
  • 634528
  • 281995
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