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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


Computer systems

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


Computer systems

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


Computer systems

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


Computer systems

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


Computer systems

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


Computer systems

2. Convert the following octal numbers to binary:

  • 65

  • 876

  • 2190

  • 67788

  • 324671

  • 4440134

  • 870145

  • 2506779


Computer systems

3. Convert the following octal numbers to decimal:

a. 90

b. 255

c. 2787

d. 44567

e. 2908043

f. 289001

g. 112009

h. 567830


Computer systems

4. Convert the following decimal numbers to octal:

  • 9

  • 32

  • 73

  • 255

  • 1,025

  • 4,099

  • 65536

  • 1,048,575


Computer systems

Convert the following octal numbers to hexadecimal:

  • 79

  • 321

  • 673

  • 2098

  • 123025

  • 401099

  • 634528

  • 281995