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 1’s Complement

In the 1’s complement format, the positive numbers remain unchanged. The negative numbers are obtained by taking the 1’s complement of the positive counterparts. For example, +9 will be represented as 00001001 in eight-bit notation, and −9 will be represented as 11110110, which is the 1’s complement of 00001001. Again, n-bit notation can be used to represent numbers in the range from −(2n−1 − 1) to +(2n−1 − 1) using the 1’s complement format. The eight-bit representation of the 1’s complement format can be used to represent decimal numbers in the range from −127 to +127.

 2’s Complement

In the 2’s complement representation of binary numbers, the MSB represents the sign, with a ‘0’ used for a plus sign and a ‘1’ used for a minus sign. The remaining bits are used for representing magnitude. Positive magnitudes are represented in the same way as in the case of sign-bit or 1’s complement representation. Negative magnitudes are represented by the 2’s complement of their positive counterparts. For example, +9 would be represented as 00001001, and −9 would be written as 11110111. Please note that, if the 2’s complement of the magnitude of +9 gives a magnitude of −9, then the reverse process will also be true, i.e. the 2’s complement of the magnitude of −9 will give a magnitude of +9. The n-bit notation of the 2’s complement format can be used to represent all decimal numbers in the range from +(2n−1 − 1) to −(2n−1. The 2’s complement format is very popular as it is very easy to generate the 2’s complement of a binary number and also because arithmetic operations are relatively easier to perform when the numbers are represented in the 2’s complement format.

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