Computer Science
Convert the following decimal numbers to binary:
(a) 23
(b) 100
(c) 145
(d) 0.25
Number System
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Answer
(a) 23
| 2 | Quotient | Remainder |
|---|---|---|
| 2 | 23 | 1 (LSB) |
| 2 | 11 | 1 |
| 2 | 5 | 1 |
| 2 | 2 | 0 |
| 2 | 1 | 1 (MSB) |
| 0 |
Therefore, (23)10 = (10111)2
(b) 100
| 2 | Quotient | Remainder |
|---|---|---|
| 2 | 100 | 0 (LSB) |
| 2 | 50 | 0 |
| 2 | 25 | 1 |
| 2 | 12 | 0 |
| 2 | 6 | 0 |
| 2 | 3 | 1 |
| 2 | 1 | 1 (MSB) |
| 0 |
Therefore, (100)10 = (1100100)2
(c) 145
| 2 | Quotient | Remainder |
|---|---|---|
| 2 | 145 | 1 (LSB) |
| 2 | 72 | 0 |
| 2 | 36 | 0 |
| 2 | 18 | 0 |
| 2 | 9 | 1 |
| 2 | 4 | 0 |
| 2 | 2 | 0 |
| 2 | 1 | 1 (MSB) |
| 0 |
Therefore, (145)10 = (10010001)2
(d) 0.25
| Multiply | = | Resultant | Carry |
|---|---|---|---|
| 0.25 x 2 | = | 0.5 | 0 |
| 0.5 x 2 | = | 0 | 1 |
Therefore, (0.25)10 = (0.01)2
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