Computer Science

Convert the following octal numbers to decimal:

(a) 257

(b) 3527

(c) 123

(d) 605.12

Number System

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Answer

(a) 257

Octal
No
PowerValueResult
7 (LSB)8017x1=7
58185x8=40
2 (MSB)82642x64=128

Equivalent decimal number = 7 + 40 + 128 = 175

Therefore, (257)8 = (175)10

(b) 3527

Octal
No
PowerValueResult
7 (LSB)8017x1=7
28182x8=16
582645x64=320
3 (MSB)835123x512=1536

Equivalent decimal number = 7 + 16 + 320 + 1536 = 1879

Therefore, (3527)8 = (1879)10

(c) 123

Octal
No
PowerValueResult
3 (LSB)8013x1=3
28182x8=16
1 (MSB)82641x64=64

Equivalent decimal number = 3 + 16 + 64 = 83

Therefore, (123)8 = (83)10

(d) 605.12

Integral part

Octal
No
PowerValueResult
58015x1=5
08180x8=0
682646x64=384

Fractional part

Octal
No
PowerValueResult
18-10.1251x0.125=0.125
28-20.01562x0.0156=0.0312

Equivalent decimal number = 5 + 384 + 0.125 + 0.0312 = 389.1562

Therefore, (605.12)8 = (389.1562)10

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