Question

what is the smallest positive (not including 0) representable number in 32-bit ieee 754 single precision floating point? show the bit encoding and the value in base 10 (fraction or decimal ok).

Answer 1

The smallest positive number in 32-bit IEEE 754 single precision floating point format is 1.401298464324817 × 10-45.

Step-by-step explanation:

The smallest positive number (not including 0) that can be represented in 32-bit IEEE 754 single precision floating point format is as follows:

Bit encoding: 0 00000001 00000000000000000000000

Value in base 10: 1.401298464324817 × 10-45

This value is obtained by using the bias of 127 for the exponent and filling the fraction bits with all zeros except for the first one, which is set to 1.