Question 1

What is IEEE 754?

Accepted Answer

IEEE 754 is the standard for floating-point arithmetic used by virtually all modern CPUs and programming languages. A number is stored as three fields: a sign bit, an exponent (biased), and a mantissa/significand. Single precision uses 32 bits; double precision uses 64 bits.

Question 2

What is the bias for single and double precision?

Accepted Answer

The exponent bias is 127 for single precision (32-bit) and 1023 for double precision (64-bit). The stored exponent value equals the true exponent plus the bias.

Question 3

How are special values like zero and infinity represented?

Accepted Answer

Zero has exponent 0 and mantissa 0. Infinity has the max exponent (all ones) and mantissa 0. NaN (Not a Number) has the max exponent and a non-zero mantissa. Subnormal numbers use exponent 0 with a non-zero mantissa.