2's Complement using C Programming

Definition

Property

Two's complement representation allows the use of binary arithmetic operations on signed integers, yielding the correct 2's complement results.

Positive Numbers

Positive 2's complement numbers are represented as the simple binary.

Negative Numbers

Negative 2's complement numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero.

Integer		2's Complement
Signed	Unsigned
5	5	0000 0101
4	4	0000 0100
3	3	0000 0011
2	2	0000 0010
1	1	0000 0001
0	0	0000 0000
-1	255	1111 1111
-2	254	1111 1110
-3	253	1111 1101
-4	252	1111 1100
-5	251	1111 1011

Note:  The most significant (leftmost) bit indicates the sign of the integer; therefore it is sometimes called the sign bit.

If the sign bit is zero,

then the number is greater than or equal to zero, or positive.

If the sign bit is one,

then the number is less than zero, or negative.

Calculation of 2's Complement

To calculate the 2's complement of an integer, invert the binary equivalent of the number by changing all of the ones to zeroes and all of the zeroes to ones (also called 1's complement), and then add one.

For example,

0001 0001(binary 17)      1110 1111(two's complement -17)
NOT(0001 0001)	=	1110 1110  (Invert bits)
1110 1110 + 0000 0001	=	1110 1111  (Add 1)

2's Complement Addition

Two's complement addition follows the same rules as binary addition.

For example,

5 + (-3)  =  2		0000 0101	=	+5
		+ 1111 1101	=	-3
		0000 0010	=	+2

Finally a C program to perform addition using 2's Complement.

#include<stdio.h>
#include<conio.h>
#include<math.h>
void showbits(int,int);

void main()
{
 int a,b,c,bit,d,e,f,g,i;
 char ch;
 do
 {
  clrscr();

  //accepting inputs
  printf("\nEnter the number of bits: ");
  scanf("%d",&bit);
  printf("Enter two numbers to be added:- \n");
  scanf("%d",&a);
  scanf("%d",&b);
  c=a+b;

  //Ones Complement
  d=~(a);
  e=~(b);

  if(a<0)
   f=a;
  else
   f=d+1;

  if(b<0)
   g=b;
  else
   g=e+1;

  //addition
  printf("\nAddition: \n");
  printf("\t ");
  showbits(f,bit);
  printf("\n");
  printf("\t+");
  showbits(g,bit);
  printf("\n\t");

  for(i=0;i<=bit;i++)
   printf("-");

  printf("\t ");
  showbits(c,bit);
  printf("\n");
  printf("\t= %d",c);

  if(c>=(-1*(pow(2,bit-1)))&&(c<=(pow(2,bit-1)-1)))
   printf("\n\nResult Status: No Overflow \n");
  else
   printf("\n\nResult Status: Overflow \n");

  printf("\n\n\nDo you wish to continue? (y/n)");

  ch=getch();
 }while(ch=='y');
}

void showbits(int n,int bit)
{
 int i,k,andmask;

 for(i=(bit-1);i>=0;i--)
 {
  andmask=1<<i;
  k=n & andmask;

  k==0?printf("0"):printf("1");
 }
}