Question

What is the smallest floating point number that can be represented using a 32-bit word?

(a) 3*10^-38

(b) 2*10^-38

(c) 0.2*10^-38

(d) 0.3*10^-38

This question was addressed to me by my college professor while I was bunking the class.

I want to ask this question from Representation of Numbers topic in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct answer is (d) 0.3*10^-38

Best explanation: Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.

Thus, the smallest floating point number that can be represented using the 32 bit number is

(1/2)*2^-127=0.3*10^-38

Thus, the smallest floating point number that can be represented using the 32 bit number is

(1-2^-23)*2^127=1.7*10^38.