Question

A combinational circuit that counts the number of occuranceof 1 bit in 4 bit input,an inout 1111 is invalid output is00,valid input is 1110 andoutput is 11, valid input is1010 and output is10 draw the truth table and k-map

Answer 1

Combinatorial circuit is in the diagram enclosed.

Truth table and Karnaugh map are first drawn.  The logical function in terms of binary variables is derived.  Then the circuit using the logic gates AND, OR, NOT  is drawn.

The circuit will be simpler with use of exclusive or gates.

X = ABC' + AC'D + BC'D + A'CD + BCD' + AB'C 
    = A(B'C + C'B) + B (C'D + D'C) + D (A C' + A' C) 

[ALSO, X' = A'B'C' + A'B' D' + A'C'D' + B'C'D' + ABCD, By taking the ‘0’s in the table] 

Y = (A'B + A B') C'D' + (A'B' + AB) C'D + CD (A'B + A B')+ (A'B'+AB)CD' 
   = (A'B + A B') (C'D' + CD) + ( A'B' + AB) (C'D + C D')