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Difference between 1’s Complement representation and 2’s Complement representation Technique

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  • Difficulty Level : Easy
  • Last Updated : 02 Nov, 2022
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Prerequisite – Representation of Negative Binary Numbers 

1’s complement of a binary number is another binary number obtained by toggling all bits in it, i.e., transforming the 0 bit to 1 and the 1 bit to 0. Examples:

Let numbers be stored using 4 bits

1's complement of 7 (0111) is 8 (1000)
1's complement of 12 (1100) is 3 (0011)

2’s complement of a binary number is 1 added to the 1’s complement of the binary number. Examples:

Let numbers be stored using 4 bits

2's complement of 7 (0111) is 9 (1001)
2's complement of 12 (1100) is 4 (0100)

  These representations are used for signed numbers.

The main difference between 1′ s complement and 2′ s complement is that 1′ s complement has two representations of 0 (zero) — 00000000, which is positive zero (+0), and 11111111, which is negative zero (-0); whereas in 2′ s complement, there is only one representation for zero — 00000000 (0) because if we add 1 to 11111111 (-1), we get 100000000, which is nine bits long. Since only eight bits are allowed, the left-most bit is discarded(or overflowed), leaving 00000000 (-0) which is the same as positive zero. This is the reason why 2′ s complement is generally used.

Another difference is that while adding numbers using 1′ s complement, we first do binary addition, then add in an end-around carry value. But, 2′ s complement has only one value for zero and doesn’t require carry values.

Range of 1’s complement for n bit number is from -2n-1-1 to 2n-1-1 whereas the range of 2’s complement for n bit is from -2n-1 to 2n-1-1.

There are 2n-1 valid numbers in 1’s complement and 2n valid numbers in 2’s complement.

Please write comments if you find anything incorrect, or if you want to share more information about the topic discussed above.

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