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Binary Addition‌

iacst-2022

Binary operations include addition, multiplication, subtraction, and division on binary digits – 0 and 1. Binary addition is applied similarly to that in the decimal system. The difference is that the decimal system uses 10 bases, whereas binary uses 2 bases.

Rules of binary addition

The following are the rules of binary addition-

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

They are similar to the decimal system, just that they use two digits only.

Procedure to perform binary addition

Let us consider an example that we need to add. First, we need to add 101 and 101 according to binary addition.

1. Place 101 and 101 one above the other, as we do for typical additions.

2. According to the binary rule, 1 + 1 = 10. Therefore, place 0 below 1 in answer position and carry over 1.

3. Now, add 0 and 0. According to binary addition, 0 + 0 = 0. However, we have 1 also as carryover. Therefore, we need to add the outcome of 0 + 0 and the carryover value 1. As a result, we get 0 + 1 = 1. Put this 1 on the left of 0 on the answer position.

4. There is no carryover. Therefore, we need to add only 1 + 1. This is equal to 10. We need to write 10 besides 1 in the answer position.

5. Therefore, the final answer of 101 + 101 = 1010 as per binary addition.

Examples of binary addition

1. Add 10001 + 11101

Solution

We need to add 10001 as per binary addition.

(+) 11101

We know the addition of 1 + 1 = 10. Therefore, place 0 below 1 on the right hand side and carryover 1. As described in the above step, we need to add all the binary units as per binary addition.

The final output we get is – 1

1 0 0 0 1

(+) 1 1 1 0 1

1 0 1 1 1 0

2. Add 11110 and 10101

Solution

We need to add 11110 and 10101 in the similar way as we did above.

Therefore, the final output is –1 1 1

1 1 1 1 0

1 0 1 0 1

1 1 0 0 1 1

Applications

1. It is used in computing applications where output is generated in only two options.

2. It is used in everyday life, like making switches, keys, electricity poles, cables, semiconductor chips, motherboards, etc.

3. Binary addition is mainly used where the output is generated mostly YES or NO.

4. It is used to make computing gates in dams and hydropower projects to convert hydel energy into electricity.

5. It is used to make various logic gates that are used in artificial intelligence these days.

6. It is helpful to make electrical circuits and control current, the voltage over a path to prevent short-circuits or electrical failure.

7. It is used to make mechanical machines in industrial and manufacturing areas.

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