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What is the 2s complement in C?

The 2s complement in C is generated from the 1s complement in C. As we know that the 1s complement of a binary number is created by transforming bit 1 to 0 and 0 to 1; the 2s complement of a binary number is generated by adding one to the 1s complement of a binary number.

In short, we can say that the 2s complement in C is defined as the sum of the one's complement in C and one.

2s complement in C

In the above figure, the binary number is equal to 00010100, and its one's complement is calculated by transforming the bit 1 to 0 and 0 to 1 vice versa. Therefore, one's complement becomes 11101011. After calculating one's complement, we calculate the two's complement by adding 1 to the one's complement, and its result is 11101100.

Let's create a program of 2s complement.

Output

2s complement in C

Analysis of the above program,

  • First, we input the number of bits, and it gets stored in the 'n' variable.
  • After entering the number of bits, we declare character array, i.e., char binary[n+1], which holds the binary number. The 'n' is the number of bits which we entered in the previous step; it basically defines the size of the array.
  • We declare two more arrays, i.e., onescomplement[n+1], and twoscomplement[n+1]. The onescomplement[n+1] array holds the ones complement of a binary number while the twoscomplement[n+1] array holds the two's complement of a binary number.
  • Initialize the carry variable and assign 1 value to this variable.
  • After declarations, we input the binary number.
  • Now, we simply calculate the one's complement of a binary number. To do this, we create a loop that iterates throughout the binary array, for(int i=0;i<n;i++). In for loop, the condition is checked whether the bit is 1 or 0. If the bit is 1 then onescomplement[i]=0 else onescomplement[i]=1. In this way, one's complement of a binary number is generated.
  • After calculating one's complement, we generate the 2s complement of a binary number. To do this, we create a loop that iterates from the last element to the starting element. In for loop, we have three conditions:
    • If the bit of onescomplement[i] is 1 and the value of carry is 1 then we put 0 in twocomplement[i].
    • If the bit of onescomplement[i] is 0 and the value of carry is 1 then we put 1 in twoscomplement[i] and 0 in carry.
    • If the above two conditions are false, then onescomplement[i] is equal to twoscomplement[i].

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