Computer Science
Perform the following conversions from decimal number to other number systems:
(a) (54)10 = (?)2
(b) (120)10 = (?)2
(c) (76)10 = (?)8
(d) (889)10 = (?)8
(e) (789)10 = (?)16
(f) (108)10 = (?)16
Number System
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Answer
(a) (54)10
| 2 | 54 | Remainder |
|---|---|---|
| 2 | 27 | 0 (LSB) |
| 2 | 13 | 1 |
| 2 | 6 | 1 |
| 2 | 3 | 0 |
| 2 | 1 | 1 |
| 0 | 1 (MSB) |
Therefore, (54)10 = (110110)2.
(b) (120)10
| 2 | 120 | Remainder |
|---|---|---|
| 2 | 60 | 0 (LSB) |
| 2 | 30 | 0 |
| 2 | 15 | 0 |
| 2 | 7 | 1 |
| 2 | 3 | 1 |
| 2 | 1 | 1 |
| 0 | 1 (MSB) |
Therefore, (120)10 = (1111000)2.
(c) (76)10
| 8 | 76 | Remainder |
|---|---|---|
| 8 | 9 | 4 (LSB) |
| 8 | 1 | 1 |
| 0 | 1 (MSB) |
Therefore, (76)10 = (114)8.
(d) (889)10
| 8 | 889 | Remainder |
|---|---|---|
| 8 | 111 | 1 (LSB) |
| 8 | 13 | 7 |
| 8 | 1 | 5 |
| 0 | 1 (MSB) |
Therefore, (889)10 = (1571)8.
(e) (789)10
| 16 | 789 | Remainder |
|---|---|---|
| 16 | 49 | 5 (LSB) |
| 16 | 3 | 1 |
| 0 | 3 (MSB) |
Therefore, (789)10 = (315)16.
(f) (108)10
| 16 | 108 | Remainder |
|---|---|---|
| 16 | 6 | 12 (C) (LSB) |
| 0 | 6 (MSB) |
Therefore, (108)10 = (6C)16.
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