CBSE Class 11 Computer Science
Question 52 of 68
Data Representation and Boolean Logic — Question 23
Back to all questions(a) 145
| Octal No | Power | Value | Result |
|---|---|---|---|
| 5 (LSB) | 80 | 1 | 5x1=5 |
| 4 | 81 | 8 | 4x8=32 |
| 1 (MSB) | 82 | 64 | 1x64=64 |
Equivalent decimal number = 5 + 32 + 64 = 101
Therefore, (145)8 = (101)10.
(b) 6760
| Octal No | Power | Value | Result |
|---|---|---|---|
| 0 (LSB) | 80 | 1 | 0x1=0 |
| 6 | 81 | 8 | 6x8=48 |
| 7 | 82 | 64 | 7x64=448 |
| 6 (MSB) | 83 | 512 | 6x512=3072 |
Equivalent decimal number = 48 + 448 + 3072 = 3568
Therefore, (6760)8 = (3568)10.
(c) 455
| Octal No | Power | Value | Result |
|---|---|---|---|
| 5 (LSB) | 80 | 1 | 5x1=5 |
| 5 | 81 | 8 | 5x8=40 |
| 4 (MSB) | 82 | 64 | 4x64=256 |
Equivalent decimal number = 5 + 40 + 256 = 301
Therefore, (455)8 = (301)10.
(d) 10.75
Integer part:
| Octal No | Power | Value | Result |
|---|---|---|---|
| 0 (LSB) | 80 | 1 | 0x1=0 |
| 1 (MSB) | 81 | 8 | 1x8=8 |
Equivalent decimal number = 8
Fractional part:
| Octal No | Power | Value | Result |
|---|---|---|---|
| 7 (LSB) | 8-1 | 0.125 | 7x0.125=0.875 |
| 5 (MSB) | 8-2 | 0.015625 | 5x0.015625=0.078125 |
Equivalent decimal number = 0.875 + 0.078125 = 0.953125
Therefore, (10.75)8 = (8.953125)10.