Perform the following operation for the binary equivalent of the decimal…
2018
Perform the following operation for the binary equivalent of the decimal numbers (−14)10 + (−15)10
The solution in 8 bit representation is :
- A.
11100011
- B.
00011101
- C.
10011101
- D.
11110011
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Correct answer: A
Solution: compute using 8-bit two's complement.
Convert -14 to 8-bit two's complement: 14 = 00001110 → invert → 11110001 → add 1 → 11110010. So -14 = 11110010.
Convert -15 to 8-bit two's complement: 15 = 00001111 → invert → 11110000 → add 1 → 11110001. So -15 = 11110001.
Add the two binary numbers: 11110010 + 11110001 = 11100011. When using two's complement, ignore the carry out of the most significant (8th) bit.
Interpret the result: 11100011 is negative. Invert → 00011100, add 1 → 00011101 which is 29, so the result is -29. This matches -14 + -15 = -29.
Final 8-bit two's complement representation: 11100011.
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