**Decimal BCD Subtractor:**

Decimal BCD Subtractor – Addition of signed BCD numbers can be performed by using 9’s or 10’s complement methods. A negative BCD number can be expressed by taking the 9’s or 10’s complement. Let us see 9’s and 10’s complement numbers and subtraction process using it.

**9’s Complement**

The 9’s complement of a decimal number is found by subtracting each digit in the number from 9. The 9’s complement of each of the decimal digits is as follows :

**9’s Complement Subtraction:**

In 9’s complement subtraction when 9’s complement of smaller number is added to the larger number carry is generated. It is necessary to add this carry to the result. (this is called an end-around carry). When larger number is subtracted from smaller one, there is no carry, and the result is in 9’s complement form and negative. This is illustrated in following examples :

The 10’s complement of a decimal number is equal to the **9’s complement ****plus 1.**

**10’s Complement Subtraction**

The 10’s complement can be used to perform subtraction by adding the minuend to the 10’s complement of the subtrahend and dropping the carry. This is illustrated in following examples.

From the above examples we can summarize steps for 9’s complement BCD subtraction as follows :

- Find the 9’s complement of a negative number
- Add two numbers using BCD addition
- If carry is generated add carry to the result otherwise find the 9’s complement of the result.

Fig. 3.34 shows the logic diagram of the circuit to implement above mentioned steps to perform BCD subtraction using 9’s complement method. As shown in the Fig. 3.34, first binary adder finds the 9’s complement of the negative number. It does this by inverting each bit of BCD number and adding 10 (1 0 1 0_{2}) to it. Let us find the 9’s complement of 2

Next two 4-bit binary adders perform the BCD addition. The last adder finds the 9’s complement of the result if carry is not generated after BCD addition otherwise it adds carry in the result. (See Fig. 3.34 on previous page).

From the above examples we can summarize steps for 10’s complement BCD subtraction as follows.

- Find the 10’s complement of a negative number
- Add two numbers using BCD addition
- If carry is not generated find the 10’s complement of the result.

Fig. 3.35 shows the logic diagram of the circuit to implement above mentioned steps to perform BCD subtraction using 10’s complement method. As shown in the Fig. 3.35, first binary adder finds the 10’s complement of the negative number (9’s complement + 1). Next two 4-bit binary adders perform the BCD addition. Finally, last 4-bit binary adder finds the 10’s complement of the number if carry is not generated after BCD addition.