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  1. GATE CS
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  3. Digital Logic

The 2's complement representation of (-539)_10 in hexadecimal is A. ABD B. DBC C. DE5 D. 9ET

GATE 2001 · Digital Logic · Number Representation · easy

Answer: DE5 in hexadecimal (option C)

  1. Convert 539 to binary (12-bit): 539 = 2^9 + 2^4 + 2^3 + 2^1 + 2^0 = 1000011011 in 10 bits. In 12 bits: 001000011011.
  2. Take 1's complement (invert all bits): 001000011011 -> 110111100100.
  3. Add 1 to get 2's complement: 110111100100 + 1 = 110111100101.
  4. Convert to hexadecimal: 110111100101 split into: 1101 | 1110 | 0101. 1101=D, 1110=E, 0101=5. Result: DE5.