What is the nearest (4+4)-bit two's-complement fixed-point binary equivalent…
2023
What is the nearest (4+4)-bit two's-complement fixed-point binary equivalent of -(3.72)₁₀ ?
- A.
0011.1100
- B.
0011.1010
- C.
1100.0100
- D.
0011.1011
Attempted by 36 students.
Show answer & explanation
Correct answer: C
In a (4+4)-bit fixed-point format, four bits are used for the integer/sign part and four bits for the fractional part.
Scale the magnitude by 2^4 = 16:
3.72 * 16 = 59.52
Using the nearest representable value, round 59.52 to 60.
60 in 8-bit binary is 00111100, so +3.75 is written as 0011.1100.
For -3.72, use the 8-bit two's complement of 00111100:
00111100 -> 11000100
Putting the fixed point after four bits gives 1100.0100. This represents -60/16 = -3.75, the nearest available 4+4 fixed-point value. Hence, Option C is correct.