Topic: Computer Organization and Architecture
Difference in dynamic range of 32-bit binary number(B) and floating point number(F) is? Standard Format for B and F as given below:
$B=$ Bit 31 Sign Bit, Bit 30-Bit0 Magnitude
$F=$ Bit 31 Sign Bit, Bit 30-Bit23 Exponent, Bit 22-Bit0 fraction
- A. $6.02(2^7-30)$ dB
- B. $6.02 (2^8-31)$ dB
- C. $6.02(2^7-31)$ dB
- D. $6.02(2^8-30)$ dB
Answer: C. $6.02(2^7-31)$ dB
Explanation: The dynamic range in decibels roughly equals $6.02 \times \text{(number of variable exponent/magnitude bits)}$. For a 32-bit integer B, the magnitude has 31 bits, yielding a dynamic range of $6.02 \times 31$ dB. For the floating-point number F, the 8-bit exponent allows values from $2^{-126}$ to $2^{127}$, spanning roughly $2^7$ powers of 2. The dynamic range is therefore dominated by the exponent, approx $6.02 \times 2^7$ dB. The difference in dynamic range is $6.02(2^7 - 31)$ dB.