UGC NET CSE | December 2014 | Part 2 | Question: 06

Question

The $\text{BCD}$ adder to add two decimal digits needs minimum of

• A. $6$ full adders and $2$ half adders
• B. $5$ full adders and $3$ half adders
• C. $4$ full adders and $3$ half adders
• D. $5$ full adders and $2$ half adders 

Answer 1

To add two decimal digits we need two 4 bit adders.

First one for adding the two BCD number and second one to make the result a valid BCD number.

Now for the first one we need a simple 4 bit adder which we can construct using 3 full adders and 1 half adder.

For the second one we need to observe how it is working,

Suppose the result obtained from 1st 4 bit adder be D₃ D₂ D₁ D₀ and also suppose this number is greater than 9. So we have to add 0110 to make it a proper BCD

Carry		C3	C2	C1	0
Result from 1st 4 bit adder	+		D3	D2	D1	D0
Adding 6	+		0	1	1	0
Final result						D0

Now D₀ will always be added with 0.So we dont need any adder for this.

Since we dont need adder for LSB ( D₀) , no carry will be generated by LSB. That means D₁ will be simply added with 1 only and this can be done by half adder.

Also D₃ will be added with C₂ only. So here too we can use half adder.

To add D₂ we will need full adder.

So total full adders = 3+1 =4  and Half adders = 1+2 = 3

So I think answer should be C)

Comments

pls tell me how to add-

A=23

B=34

 i got your soln but can u pls explain it with this example

@Digvijaysingh Gautam 

@ Shaik Masthan??

 

 

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The carry out of ones sum will be used as carry in of tens addition. You'll need Four Full adders in your first adder. So There will be 5 full adders and 2 half adders.

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I tried to add 5 and 5 in BCD and carry is generated on and carry is generated at MSB i think answer should be B as there also FA should be used.

Correct me if I am wrong😁

Answer 2

The final carry generated by adding Ones digits will be made carry-in for addition of Tens digits, hence, the A0 + B0 is a full adder. So you require 5 Full adders and 2 Half adders. Option D is the right answer.

Comments

1001(A0)  + 1001(B0)  = 1  0010   we add 0110  to make it valid

ans will be 0010 + 0110= 1  1000 =18

another example 0110 +111 = 1101 again we add 0110  to get  1 0011

where this final carry is added to A0 , B0

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The final carry is added through the $C_{in}$ in FA of $A_0,B_0$ when the TENS place data is flown in the circuit.

Answer 3

Ans : D

ref: https://books.google.co.in/books?id=5LNwVRpfkRgC&pg=PA177&lpg=PA177&dq=BCDBCD+adder+to+add+two+decimal+digits+needs&source=bl&ots=g5ooFSiKoY&sig=RekqrKWdjPhsuxEcWQjeuFb0usM&hl=en&sa=X&ved=0ahUKEwiOgJzQ5vvVAhUIto8KHTekCpYQ6AEIUTAH#v=onepage&q=BCDBCD%20adder%20to%20add%20two%20decimal%20digits%20needs&f=false

Comments

In the question given at link the option D is none of these. But here it is not so. So how it is option D here.. would you please explain... According to me correct answer should be 7 full adders and one half adder which is not in options

Answer 4

For Binary addition, 3 full adders and 1 half adder is required. And then BCD conversion needs 6 to be added, which in turn requires 2 more full adders and 1 half adder.

Thus, Final Answer is "D" - 5 Full adders and 2 Half adders