Updated 9/30/2002
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1. For each of the following binary floating-point numbers, supply the equivalent value as a base 10 fraction, and then as a base 10 decimal. The first problem has been done for you:
| Binary Floating-Point | Base 10 Fraction | Base 10 Decimal |
| 1.101 (sample) | 1 5/8 | 1.625 |
| 11.11 | ||
| 1.1 | ||
| 101.001 | ||
| 1101.0101 | ||
| 1110.00111 | ||
| 10000.101011 | ||
| 111.0000011 | ||
| 11.000101 |
2. For each of the following exponent values, shown here in decimal, supply the actual binary bits that would be used for an 8-bit exponent in the IEEE Short Real format. The first answer has been supplied for you:
| Exponent (E) | Binary Representation |
|
2 (sample)
|
10000001 |
|
5
|
|
|
0
|
|
|
-10
|
|
|
128
|
|
|
-1
|
3. For each of the following floating-point binary numbers, supply the normalized value and the resulting exponent. The first answer has been supplied for you:
| Binary Value | Normalized As | Exponent |
| 10000.11 (sample) | 1.000011 | 4 |
| 1101.101 | ||
| .00101 | ||
| 1.0001 | ||
| 10000011.0 | ||
| .0000011001 |
4. For each of the following floating-point binary examples, supply the complete binary representation of the number in IEEE Short Real format. The first answer has been supplied for you:
Binary Value |
Sign, Exponent, Mantissa |
| -1.11 (sample) | 1 01111111 11000000000000000000000 |
| +1101.101 | |
| -.00101 | |
| +100111.0 | |
| +.0000001101011 |