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 | Power | Value | Result |
|---|---|---|---|
| 7 (LSB) | 80 | 1 | 7x1=7 |
| 5 | 81 | 8 | 5x8=40 |
| 2 (MSB) | 82 | 64 | 2x64=128 |
Equivalent decimal number = 7 + 40 + 128 = 175
Therefore, (257)8 = (175)10
(b) 3527
| Octal No | Power | Value | Result |
|---|---|---|---|
| 7 (LSB) | 80 | 1 | 7x1=7 |
| 2 | 81 | 8 | 2x8=16 |
| 5 | 82 | 64 | 5x64=320 |
| 3 (MSB) | 83 | 512 | 3x512=1536 |
Equivalent decimal number = 7 + 16 + 320 + 1536 = 1879
Therefore, (3527)8 = (1879)10
(c) 123
| Octal No | Power | Value | Result |
|---|---|---|---|
| 3 (LSB) | 80 | 1 | 3x1=3 |
| 2 | 81 | 8 | 2x8=16 |
| 1 (MSB) | 82 | 64 | 1x64=64 |
Equivalent decimal number = 3 + 16 + 64 = 83
Therefore, (123)8 = (83)10
(d) 605.12
Integral part
| Octal No | Power | Value | Result |
|---|---|---|---|
| 5 | 80 | 1 | 5x1=5 |
| 0 | 81 | 8 | 0x8=0 |
| 6 | 82 | 64 | 6x64=384 |
Fractional part
| Octal No | Power | Value | Result |
|---|---|---|---|
| 1 | 8-1 | 0.125 | 1x0.125=0.125 |
| 2 | 8-2 | 0.0156 | 2x0.0156=0.0312 |
Equivalent decimal number = 5 + 384 + 0.125 + 0.0312 = 389.1562
Therefore, (605.12)8 = (389.1562)10
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