Question

What is the mantissa and exponent respectively obtained when we add 5 and 3/8 in binary float point representation?

(a) 0.101010,011

(b) 0.101000,011

(c) 0.101011,011

(d) 0.101011,101

This question was posed to me during an interview.

This question is from Representation of Numbers in chapter Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Right option is (c) 0.101011,011

The best I can explain: We can represent the numbers in binary float point as

5=0.101000(2^011)

3/8=0.110000(2^101)=0.000011(2^011)

=>5+3/8=(0.101000+0.000011)(2^011)=(0.101011)(2^011)

Therefore mantissa=0.101011 and exponent=011.