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 |
1 5/8
|
1.625 |
| 11.11 |
3 3/4
|
3.75 |
| 1.1 |
1 1/2
|
1.5 |
| 101.001 |
5 1/8
|
5.125 |
| 1101.0101 |
13 5/16
|
13.3125 |
| 1110.00111 |
14 7/32
|
14.21875 |
| 10000.101011 |
16 43/64
|
16.671875 |
| 111.0000011 |
7 3/128
|
7.0234375 |
| 11.000101 |
3 5/64
|
3.078125 |
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
|
10000001
|
|
5
|
10000100
|
|
0
|
01111111
|
|
-10
|
01110101
|
|
128
|
11111111
|
|
-1
|
01111110
|
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 | 1.000011 | 4 |
| 1101.101 | 1.101101 | 3 |
| .00101 | 1.01 | -3 |
| 1.0001 | 1.0001 | 0 |
| 10000011.0 | 1.0000011 | 7 |
| .0000011001 | 1.1001 | -6 |
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 | 1 01111111 11000000000000000000000 |
| +1101.101 | 0 10000010 10110100000000000000000 |
| -.00101 | 1 01111100 01000000000000000000000 |
| +100111.0 | 0 10000100 00111000000000000000000 |
| +.0000001101011 | 0 01111000 10101100000000000000000 |