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GATE Overflow Test Series | Digital Logic | Test 1 | Question: 26

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The decimal and hexadecimal representation for the bit string $110000100101$, represented in $16-bit$ $1's$ complement representation are:

  1. $-986,\texttt{0xFC25}$
  2. $3109,\texttt{0xFC25}$
  3. $3109,\texttt{0xF3DA}$
  4. $986,\texttt{0xF3DA}$
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In $1's$ complement representation, negative numbers are represented by inverting their bits (no taking of complement for positive numbers as in $2's$ complement representation). Since the leading bit is $1,$ the number is negative here. So, we invert every bit and get the value as $0011\;1101\;1010 = 2^{9}+2^8+2^7+2^6+2^4+2^3+2^1 =2^{10} - 2^{6}+26 = 1024 - 64 + 26 =986.$
    
    So, the represented decimal value is $-986.$
    
    Hexadecimal value in 16 bits $=\underbrace{1111}_F\; \underbrace{1100}_{C}\;\underbrace{0010}_{2}\;\underbrace{0101}_{5} = (FC25)_{16}$
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