Binary Arithmetic:

The arithmetic operations-addition, subtraction, multiplication and division, performed on the binary numbers is called Binary arithmetic. In computer system, the basic arithmetic operation performed on the binary numbers is Binary addition and Binary Subtraction.

In the following section, we will discuss the binary addition and binary subtraction.

Binary Addition:

Binary addition involves of two or more binary numbers. The binary addition rules are used while performing the binary addition. The following table shows the binary additions rules.

Binary Addition Rules

Input 1Input 2SumCarry0 0 no carry 0 1 1 no carry 1 0 1 no carry 1 1 0 1

Binary addition of three inputs, when all the inputs are 1, follows the rules show in table.

Binary addition of three inputs

Input 1Input 2Input 3SumCarry1 1 1 1 1

Adding the binary numbers involves the following steps:

1. Start adding by adding the bits in the unit’s column (the rightmost column). Use the rules of binary addition.

2. The result of adding bits of a column is asum, with or without acarry.

3. Write thesumin the result of that column.

4. Ifcarryis present, thecarryis carried-over to the addition of the next left column.

5. Repeat steps 2 to 4 for each column, i.e. the tens column, hundreds column and so on.

Example:

When we add 0 and 1 in the units’ column, sum is 1 and there is no carry. The sum 1 is written in the units’ column of the result. In the Tens column, we add 1 and 0 to get the sum 1. There is no carry. The sum 1 is written in the tens column of the result.

Binary Addition ........................Decimal Addition

....... 1 0 ..................................... 2

.....+ 0 1 .................................+ 1Result1 ............................Result3

Binary Subtraction:

Binary subtraction involves subtraction of two binary numbers. The binary subtraction rules are used while performing the binary subtraction. The binary subtraction rules are shown below.

Binary subtraction rules

Input 1Input 2DifferenceBorrow0 0 0 no borrow 0 1 1 1 1 0 1 no borrow 1 1 0 no borrow

The steps for performing subtraction of binary numbers are as follow:

1. Start subtraction by subtracting the bits in the lower row from the upper row, in the units’ column.

2. Use the binary subtraction rule. If the bit in the upper row is less than the lower row,borrow1 from the upper row of the next column (on the left side). The result of subtracting two bits is thedifference.

3. Write thedifferencein the result of that column.

4. Repeat step 2 and 3 for each column, I.e. the tens column, hundreds column and so on.

Example:

Subtract 01 from 11. Verify the answer with the help of decimal subtraction.

When we subtract 1 from 1 in the Units column, the difference is 0. Write the difference in the Units column of the result. In the Tens column, subtract 0 from 1 to get the difference 1. Write the difference in Tens column of the result.

Binary Subtraction ................... ....Decimal Subtraction

........1 1 ...............................................3

- 0 1 .............................................- 1

Result1 0.....................................Result2

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