To determine the range of the exponent for a 32-bit floating-point number with a 7-bit signed exponent, we need to understand how signed integers work and how they are represented.
1. **Representation of the Signed Exponent:**
- A 7-bit signed exponent can represent values using two's complement notation.
- In two's complement, the range for a signed \( n \)-bit number is from \(-2^{(n-1)}\) to \(2^{(n-1)} - 1\).
2. **Calculation:**
- For a 7-bit signed exponent:
- The smallest value is \(-2^{(7-1)} = -2^6 = -64\).
- The largest value is \(2^{(7-1)} - 1 = 2^6 - 1 = 63\).
Thus, the range of the 7-bit signed exponent is from \(-64\) to \(63\).
