Digital

Binary Addition: Rules And its Examples

A binary is a number system. In binary system there are only two numbers and these are represented by 0 and 1 with the radix 2 i.e. (100110)2. The region behind of the radix 2 is that because binary only use two digits that are “0” and “1”. All digital devices use binary number system. The binary addition is binary arithmetic operation; it is a mathematical operation that performs the addition of two or more than two operand. The binary arithmetic operations are binary addition, subtraction, multiplication, and division, play an important role in electronics devices. In this tutorial we are going to discuss the binary addition and two the addition operation performed.

The operation of binary addition is very similar concept to the base 10 decimal number system. The binary number system consist only two digits. In modern time all digital computer use binary number system.  The four types of binary operation occur in binary asthmatic that is binary addition binary subtraction binary multiplication and binary division. Before performing the binary addition operation firstly we should understand the complete knowledge of how the place works in the binary number system. In binary number system the bit “0” represents the “LOW” state, and the binary bit 1 represents the “HIGH” state.

Decimal vs Binary

Here are some equivalent values of decimal vs binary:

 Decimal Binary 0 0 1 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111

It is much easier than the decimal addition when you follow the rules and trick. Here bellow the some rule you can remember it and follow it. Binary additions have five rules these are given below;

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 =10
• 1 + 1 +1 = 11

Binary addition is the same process as decimal. To add 7 + 2, you do the following steps:

1. Convert the 7 to 0111
2. Convert the 2 to 0010
3. Add the ones column, e.g. 1 + 0 = 1
4. Add the twos column, e.g. 1 + 1 = 10
5. Carry the 1 into the fours column and leave the 0 in the twos column
6. Add the twos column, e.g. 1 + 1 + 0 = 10
7. Carry the 1 into the eights column and leave the 0 in the fours column
8. Add the eights column, e.g. 1 + 0 + 0 = 1

Here some process for binary addition 101+101

Procedure for Binary Addition of Numbers:

101

(+) 101

First consider the column1’s, (1+1) and add the one’s column, it gives the result 10 as per the binary rule of addition.
Now, leave the 0 in the one’s column and the carry will be “1”.

1
101
(+) 101

0

Now add 10’s place, 1+ ( 0 + 0 ) = 1. So, no carry produce, the value 1 in the 10’s place

1

101

(+) 101

10

Now add the 100’s place ( 1 + 1 ) = 10. Leave the value 0 in the 100’s place and carries 1 to the 1000’s place.

1

101

(+) 101

1010

The result of the binary addition is 1010.
When you cross check the result of binary addition. The value of binary change in decimal value you get the same result.
So, 5 + 5 = 10
The 10 decimal value is equal in binary is 1010.

The table of binary adding of two numbers is given below:

 X Y X + Y 0 0 0 0 1 1 1 0 1 1 1 10      (where 1 is carried over)

Addition of two Signed Binary Numbers

Let us consider two signed binary digits A & B, and it is represented in 2’s complement form. Here we are going to perform the two bit signed binary number addition. It is most similar to the addition of two bits signed binary number except the resultant sum contains carry out from sign bits and we get correct result.

If the result is positive number you can identify the magnitude of it directly but if result is negative than take 2’s complement of the result to find the correct magnitude.

Example 1

Now we are performing the addition of two decimal numbers +7 and +4.

+710 = 001112

+410 = 001002

The addition of these two numbers is

+710    +   +410 = 00111+ 001002

+710     +  +410 = 010112.

The resultant contains 5 bits. There is no carry generate from the addition hence ‘0’ indicates that the resultant sum is positive. So, the magnitude of two bits binary addition in decimal is 11. Therefore, the addition of two positive numbers will obtain another positive number.

Example 2

Now we are going to perform the addition of two decimal numbers -7 and -4 using 2’s complement method.
Firstly we convert the -7 and -4 into 2’s complement number. These are shown below.

−710 = 110012

−410 = 111002

The addition of these two numbers is

−710     +    −410 = 1110012 + 111002

−710     +    −410 = 1101012.

The resultant contains 6 bits. In this case, the sixth bit shows the carry bit and the carry bit show the negative sign of the resultant sum, so we can remove it from result. After removing the carry bit the resultant is 101012.

In this addition, the bit generated and it is ‘1’ that indicates the resultant sum is negative. So, by taking 2’s complement of it we will get the magnitude of resultant sum in decimal number system is 11. Therefore, the addition of two positive numbers will obtain another positive number.

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