What is the decimal value of the floating-point number C1D00000 (hexadecimal…
2011
What is the decimal value of the floating-point number C1D00000 (hexadecimal notation)? (Assume 32-bit, single precision floating point IEEE representation)
- A.
28
- B.
-15
- C.
-26
- D.
-28
Attempted by 75 students.
Show answer & explanation
Correct answer: C
To convert the hexadecimal value C1D00000 to decimal using IEEE 754 single-precision floating-point representation, first convert the hex value to binary: 1100 0001 1101 0000 0000 0000 0000 0000.
Identify the sign bit (first bit): 1 indicates a negative number. Extract the exponent bits (next 8 bits): 10000011, which is 131 in decimal. Subtract the bias (127) to get the actual exponent: 131 - 127 = 4.
Extract the mantissa bits (remaining 23 bits): 101 followed by zeros, representing 1.625 (calculated as 1 + 1/2 + 1/8). Calculate the final value: -1 × 1.625 × 2^4 = -1 × 1.625 × 16 = -26.
A video solution is available for this question — log in and enroll to watch it.