✅ IEEE 754 Double Precision Format:

The **exponent** field in the IEEE 754 double precision (Binary 64) format is 11 bits long and uses a **bias of 1023**.

✅ Step-by-Step Explanation:

• The exponent field has **11 bits**, which means it can represent values between **0 and 2047**.
• The exponent is stored in **biased form**: the stored value is the actual exponent + 1023.
• For **normalized numbers**, the exponent range is:
• Minimum exponent: \( 1 - 1023 = -1022 \)
• Maximum exponent: \( 2046 - 1023 = +1023 \)
• Special cases:
• **Exponent = 0**: Used for **denormalized numbers**.
• **Exponent = 2047**: Represents **infinity** or **NaN** (Not a Number).

✅ Final Answer:

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

From -1022 to +1023 (for normalized numbers)