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For a binary half sub tractor having two inputs A and B, the correct set of logical expressions for the outputs D (= A minus B) and X (= borrow) are
(a)π· = π΄ π΅ + π΄Μ
π΅, π = π΄Μ
π΅
(b)π· = π΄Μ
π΅ + π΄ π΅Μ
+ π΄ π΅Μ
, π = π΄ π΅Μ
(c)π· = π΄Μ
π΅ + π΄ π΅Μ
, π = π΄Μ
π΅
(d)π· = π΄ π΅ + π΄Μ
π΅Μ
, π = π΄ π΅Μ
Answer is ( c )
Concept
For a binary half sub-tractor , please find the below truth table :

To write down the Boolean expression for the same :
D = f(A,B)= f_{1} + f_{2} \implies D = π΄Μ π΅ + π΄ π΅Μ ,
X = f(A,B)= f_{1} \implies π = π΄Μ π΅
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