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# Is it possible to compute -12 (decimal) in 4 bits binary

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Problem Detail:

This is what I have so far

1 1 0 0

Switch values by 2s Complement

0 0 1 1 + 1

0 1 0 0

#### Answered By : DylanSp

No, it's not possible, at least using the standard representations. An unsigned \$n\$-bit number can represent any integer in the interval \$[0, 2^{n} - 1]\$. A signed \$n\$-bit number using two's complement can represent integers in the interval \$[-2^{n - 1}, 2^{n - 1} - 1]\$. With \$n = 4\$, that gives an interval of \$[-8, 7]\$, which obviously doesn't include \$12\$. One's complement can use \$n\$ bits to represent the interval \$[-(2^{n - 1} - 1), 2^{n - 1} - 1]\$, giving the interval \$[-7, 7]\$ for four bits, which also doesn't work. You'd have to contrive a nonstandard representation to represent \$-12\$ in four bits.

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Question Source : http://cs.stackexchange.com/questions/53274

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