Phrases Previous Year Questions (PYQs) – Floating Point Representation

10-bit Floating Point: +∞ Representation

Format: The 10-bit floating point is structured as follows:

• 1 bit for sign (S)
• 5 bits for exponent (E)
• 4 bits for fraction/mantissa (F)

IEEE Rule for +∞:

In IEEE floating-point format, +∞ is represented as:

• Sign bit (S): 0
• Exponent bits (E): all 1s → 11111
• Fraction bits (F): all 0s → 0000

✅ Final 10-bit Representation: 0111110000

✅ 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)