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Binary Half Subtractor

Ask
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)𝐷 = 𝐴  π΅ + 𝐴̅  π΅,   𝑋 = 𝐴̅ 𝐡
(b)𝐷 = 𝐴̅  π΅ + 𝐴 𝐡̅ + 𝐴 𝐡̅, 𝑋 = 𝐴 𝐡̅
(c)𝐷 = 𝐴̅  π΅ + 𝐴 𝐡̅,  π‘‹ = 𝐴̅ 𝐡
                  (d)𝐷 = 𝐴  π΅ + 𝐴̅ 𝐡̅,  π‘‹ = 𝐴 𝐡̅
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΅ + 𝐴 𝐡̅,  
           X = f(A,B)= f_{1} \implies  π‘‹ = 𝐴̅ 𝐡


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