Computer Science – 13.3 Floating-point numbers, representation and manipulation | e-Consult
13.3 Floating-point numbers, representation and manipulation (1 questions)
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Conversion Steps:
- Sign Bit: The number 65.5 is positive, so the sign bit is 0.
- Exponent: We need to find the power of 2 that gives us 65.5. 26 = 64, so the exponent is 6. Adding the bias of 127 gives us 6 + 127 = 133. In binary, 133 is 10000101.
- Mantissa: Convert 65.5 to binary: 65.5 = 1000001.1. Add the implicit '1' to get 1.10000011. We only store the first 23 bits, so the mantissa is 1.10000011.
Table Representation:
| Cell | Value |
| Sign Bit | 0 |
| Exponent | 10000101 |
| Mantissa | 1.10000011 |