Computer Systems

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# Computer Systems - PowerPoint PPT Presentation

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

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

• 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

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

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

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

2. Convert the following octal numbers to binary:

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

3. Convert the following octal numbers to decimal:

a. 90

b. 255

c. 2787

d. 44567

e. 2908043

f. 289001

g. 112009

h. 567830

Convert the following octal numbers to hexadecimal:

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