Discussion
For a 'n' bit number, the maximum positive number which can be represented in 1's complement representation is :
Answer: C
The maximum positive number is \(2^{n-1} - 1\).
In 1's complement the most significant bit is the sign bit, 0 for positive, so only n - 1 bits remain for the magnitude. The largest positive value is a 0 followed by n - 1 ones:
\[ 0\,111\ldots1 = 2^{n-1} - 1 \]
For 8 bits that is 01111111 = 127. The range is \(-(2^{n-1}-1)\) to \(+(2^{n-1}-1)\), with two zeros. \(2^{n}\) and \(2^{n+1} - 1\) need more bits than are available, and \(2^{n-1}\) is one more than the largest value.
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