Computer Science
Convert the following binary numbers to decimal:
(a) 1101
(b) 111010
(c) 101011111
Number System
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Answer
(a) 1101
| Binary No | Power | Value | Result |
|---|---|---|---|
| 1 (LSB) | 20 | 1 | 1x1=1 |
| 0 | 21 | 2 | 0x2=0 |
| 1 | 22 | 4 | 1x4=4 |
| 1 (MSB) | 23 | 8 | 1x8=8 |
Equivalent decimal number = 1 + 4 + 8 = 13
Therefore, (1101)2 = (13)10
(b) 111010
| Binary No | Power | Value | Result |
|---|---|---|---|
| 0 (LSB) | 20 | 1 | 0x1=0 |
| 1 | 21 | 2 | 1x2=2 |
| 0 | 22 | 4 | 0x4=0 |
| 1 | 23 | 8 | 1x8=8 |
| 1 | 24 | 16 | 1x16=16 |
| 1 (MSB) | 25 | 32 | 1x32=32 |
Equivalent decimal number = 2 + 8 + 16 + 32 = 58
Therefore, (111010)2 = (58)10
(c) 101011111
| Binary No | Power | Value | Result |
|---|---|---|---|
| 1 (LSB) | 20 | 1 | 1x1=1 |
| 1 | 21 | 2 | 1x2=2 |
| 1 | 22 | 4 | 1x4=4 |
| 1 | 23 | 8 | 1x8=8 |
| 1 | 24 | 16 | 1x16=16 |
| 0 | 25 | 32 | 0x32=0 |
| 1 | 26 | 64 | 1x64=64 |
| 0 | 27 | 128 | 0x128=0 |
| 1 (MSB) | 28 | 256 | 1x256=256 |
Equivalent decimal number = 1 + 2 + 4 + 8 + 16 + 64 + 256 = 351
Therefore, (101011111)2 = (351)10
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