9 digit floating point number conversion

Question

1. Format A There is 1 sign bit. There are k = 5 exponent bits. The exponent bias is 15. There are n = 3 fraction bits.

Those are the special ieee parameters

Binary number 1 00111 010

After all the math I get -5/1024

However, my buddy got -704

Who is right?

Answer 1

As the calculation below shows, it appears that you are correct, and the correct answer is -5/1024:

Input: 1 00111 010
Mantissa: 1.010 base 2
Exponent: 111 base 2 = 7 base 10; 7 − 15 = -8
De-normalize: 1.010 base 2 × 2^-8 = .00000001010

The following table shows how you can convert the denormalized number into a base 10 decimal:

Exponent |    2^-8    |    2^-9     |    2^-10     |     2^-11     |
Decimal  | 0.00390625 | 0.001953125 | 0.0009765625 | 0.00048828125 |
Bit      |     1      |     0       |      1       |      0        |
Value    | 0.00390625 |     0       | 0.0009765625 |      0        |

Total = 0.00390625 + 0.0009765625 = 0.0048828125

This value must then be negated because the sign bit is set. So the final result is -0.0048828125. This equals -5/1024 which you originally got.

Here is a link to a great site which shows how to do the conversion step by step.