1’s and 2’s complement of a Binary Number
Given a Binary Number as a string, print its 1’s and 2’s complements.
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.In the
1’s complement format , the positive numbers remain unchanged . The
negative numbers are obtained by taking the 1’s complement of 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.
Examples:
1's complement of "0111" is "1000"
1's complement of "1100" is "0011"
2’s complement of a binary number is 1, added to the 1’s complement of
the binary number. In the 2’s complement representation of binary
numbers, the MSB represents the sign with a ‘0’ used for 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.
Examples:
2's complement of "0111" is “1001"
2's complement of "1100" is “0100"
Another trick to finding two’s complement:
Step 1: Start from the Least Significant Bit and traverse left until you find a
1. Until you find 1, the bits stay the same
Step 2: Once you have found 1, let the 1 as it is, and now
Step 3: Flip all the bits left into the 1.
Illustration
Suppose we need to find 2s Complement of 100100
Step 1: Traverse and let the bit stay the same until you find 1. Here x is not
known yet. Answer = xxxx00 –
Step 2: You found 1. Let it stay the same. Answer = xxx100
Step 3: Flip all the bits left into the 1. Answer = 011100.
Hence, the 2s complement of 100100 is 011100.
For one’s complement, we simply need to flip all bits.
For 2’s complement, we first find one’s complement. We traverse the one’s
complement starting from LSB (least significant bit), and look for 0. We flip
all 1’s (change to 0) until we find a 0. Finally, we flip the found 0. For
example, 2’s complement of “01000” is “11000” (Note that we first find
one’s complement of 01000 as 10111). If there are all 1’s (in one’s
complement), we add an extra 1 in the string. For example, 2’s complement
of “000” is “1000” (1’s complement of “000” is “111”).
