Question

The range of the exponent E in the IEEE 754 double precision (Binary 64) format is:

• A. -1023 \(≤\) E \(≤\) 1023
• B. -1022 ≤ E ≤ 1022
• C. -1023 ≤ E ≤ 1022
• D. -1022 ≤ E ≤ 1023

Hint:

The exponent in IEEE 754 double precision is stored with a bias of 1023. The actual exponent is the stored value minus the bias.

Answer 1

The Correct Option is D

In the IEEE 754 double precision (64-bit) format, the exponent \( E \) is stored with a bias of 1023. This means the actual exponent is \( E - 1023 \).
The exponent is represented by an 11-bit number, so the range of \( E \) is from \( 0 \) to \( 2047 \). 
However, when taking the bias into account, the actual exponent range is from \( -1022 \) to \( 1023 \). Thus, the range of \( E \) is: \[ \boxed{-1022 \leq E \leq 1023}. \]