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GATE Overflow Test Series | Digital Logic | Test 1 | Question: 25

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The $16$ bit $2's$ complement representation and the hexadecimal representation after finding 2's complement of the decimal number $2688,$ respectively are:
  1. $0000\;1010\;1000\;0000,\texttt{0xF580}$
  2. $1111\;0101\;1000\;0000,\texttt{0x0A80}$
  3. $1111\;0101\;1000\;0000,\texttt{0xF580}$
  4. $0000\;1010\;1000\;0000,\texttt{0x0A80}$
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In $2's$ complement representation for signed numbers, positive numbers are represented as is in binary and negative numbers are represented in their $2's$ complement form.

$2688 = 2048 + 512 + 128 = 0000\;1010\;1000\;0000.$

$2's$ complement of $2688 = \underbrace{1111}_{F}\;\underbrace{0101}_{5}\;\underbrace{1000}_{8}\;\underbrace{0000}_{0} = (F580)_{16}$

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