Page 6 - 8-Math-3 Number Systems

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(iii) Conversion from Octal System to Decimal System:
Consider the following examples.

Example: Write the following octal numbers as decimal numbers.

(i) (126)8 (ii) (424002)8
Solution:

(i) (126)8
(126)8 = 1 x 82 + 2 x 81 + 6 x 8°
= 1 x64 + 2 x 8 + 6 x 1

= 64 + 16 + 6 = 86

(ii) (424002)8 = 4 x 85 + 2 x 84 + 4 x 83 + 0 x 82 + 0 x 81 + 2 x 8°
= 4 x 32768 + 2 x 4096 + 4x512 + 0 + 0 + 2 x 1

= 131072 + 8192 + 2048 + 0 + 0 + 2

= 141314

EXERCISE 3.1

1. Convert the following into decimal system.

(i) (101)2 (ii) (2044)5 (iii) (1101110)2

(iv) (7016)8 (v) (2360)8 (vi) (1011010100)2

(vii) (1001001)2 (viii) (3100)5

2. Convert the following into the base system as indicated against each question.
(i) 3025 to binary, octal and base 5 (ii) (671)8 to binary and base 5
(iii) (2006)8 to binary and base 5
(iv) 867 to binary, octal and base 5
(v) (10011001) to octal and base 5

3.2.2 Adding, Subtracting and Multiplying Numbers with Base 2:

(a) Binary Number System (Base 2):
Addition: We know that in the binary number system only two digits 0 and 1 are used.

version: 1.1

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