Binary Arithmetic

Binary Arithmetic
Binary Addition
The four basic rules for adding binary digits (bits) are as follows:
0+0=0 Sum of 0 with a carry 0
0+1=1 Sum of 1 with a carry 0
1+0=1 Sum of 1 with a carry 0
1+1=1 0 Sum of 0 with a carry 1
Examples:
110 6 111 7 1111 15
100 4 011 3 1100 12
_____ _____ _____ _____ _____ ___
1010 10 1010 10 11011 27

Binary Subtraction
The four basic rules for subtracting are as follows:
0-0=0
1-1=0
1-0=1
0-1=1 with a borrow of 1
Examples:
11 3 11 3 101
01 1 10 2 011
_____ _____ _____ _____ _____
10 2 01 1 010

5 110 6 101101 45
3 101 5 001110 14
_____ _____ _____ _____ _____
2 001 1 011111 31

1 s and 2 s Complement of Binary Number
The 1 s complement and the 2 s complement of binary number are important because they permit the representation of negative numbers.
Binary Number 1 0 1 1 0 0 1 0





1 sComplement 0 1 0 0 1 1 0 1
2 s Complement of a binary number is found by adding 1 to the LSB of the 1 s Complement.
2 s Complement= (1 s Complement) +1

Binary number 10110010
1 scomplement 01001101
Add 1 + 1
----------------------------------------
2 s complement 01001110

Subtraction Using 2 s complement Method
Subtraction is a special case of addition. For example, subtracting +6 (the subtrahend) from +9 (the minuend) is equivalent to adding -6 to +9. Basically, the subtraction operation changes the sign of the subtrahend and adds it to the minuend. The result of a subtraction is called the difference.

The sign of a positive or negative binary number is changed by taking its 2 s
Complement.

For example, when you take the 2 s complement of the positive number (00000100)2 (+4), you get (11111100)2.