GATE CSE 1990 | Question: 1-i

Question

Fill in the blanks:

In the two bit full-adder/subtractor unit shown in below figure, when the switch is in position $2$ ___________ using _________ arithmetic.

 

Comments

Switch in position 1: A + B
Switch in position 2: A - B ( A+ 2's complement of B)

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Similar question

https://gateoverflow.in/937/gate2003-46

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The answer itself is written in gate overflow book in the question’s daigram.

Answer 1

When the switch is at position $2,$ it is connected to $V_{cc}$  thus, the value of control input $M = 1$ which is fed to XOR gates as well. So

• $B_1 \oplus  1  = \overline{B_1}$ and
• $B_0 \oplus 1  = \overline{B_0}$

And the basic hardware is of adder only.

Now $C_{in}$ is connected to $V_{cc}$  as well. Hence,  $C_{in}  =  1.$

Net operation can be denoted as :  $S_0  =  A_0 + \overline{B_0} + 1$  and similarly for $S_1$ as well.

This is nothing but an expression of subtraction using $2's$ complement. $($Had it been $A_0 + \overline{B_0},$ it would have been addition of $1's$ complement merely, but for subtraction we need to have $2's$ complement of other operand which is $B$ here$)$

Hence, the correct answer should be : subtraction, 2's complement

Comments

This answer hasn't been updated in GO pdf!!

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Because 2's complement is (1's complement +1). So, B= $B_1B_o$.

2's complement of B = B'+1 = $\bar{B_1}\bar{B_0}+1$

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why is so =A0+complement(B0)+1

 

it should be (A0 xor B0 xor C0) that is it should(A0 xor B0 xor 1 ) right