Question

7-bit float to fraction

Consider a 7-bit float representation with 3 exponent bits. that k is the number of exponent bits, and the bias is computed as 2^k-1-1.

For each problem, convert the given float value (provided as a series of bits) into the equivalent base 10 fraction. Simplify each fraction as much as possible. If there is a whole number part and a fractional part, put a space between them.

Here are some example values in the correct format:

• 12 1/2
• 13/16
• -7

Need help with these

1.Convert 0 000 101 to a base 10 fraction.

2.Convert 0 011 010 to a base 10 fraction.

3.Convert 1 011 001 to a base 10 fraction

4.Convert 0 010 000 to a base 10 fraction

5.Convert 1 000 010 to a base 10 fraction.

6.Convert 1 011 000 to a base 10 fraction.

7.Convert 1 110 111 to a base 10 fraction.

8.Convert 1 101 001 to a base 10 fraction.

9.Convert 0 000 010 to a base 10 fraction.

10.Convert 0 001 111 to a base 10 fraction.

Answer 1

Solution:

The Conversion Procedure as follows:

1. If the original number is in hex, convert it to binary.
2. Separate into the sign, exponent, and mantissa fields.
3. Extract the mantissa from the mantissa field, and restore the leading one. You may also omit the trailing zeros.
4. Extract the exponent from the exponent field, and subtract the bias to recover the actual exponent of two. As before, the bias is 2k−1 − 1, where k is the number of bits in the exponent field, giving 3 for the 8-bit format and 127 for the 32-bit.
5. De-normalize the number: move the binary point so the exponent is 0, and the value of the number remains unchanged.
6. Convert the binary value to decimal. This is done just as with binary integers, but the place values right of the binary point are fractions.
7. Set the sign of the decimal number according to the sign bit of the original floating point number: make it negative for 1; leave positive for 0.