Combinational Lo Unit – 2 Session - 5 Combinational ... - Book Spar

www.bookspar.com | VTU NOTES | QUESTION PAPERS | NEWS | RESULTS | FORUMS10CS 33 LOGIC DESIGNWe can simplify itUNIT – 2 Combinational Logic CircuitsY= A’ . B + A . B’ + A . B + A . B= A’ . B + A . B + A . B’ + A . B= B . (A’ + A) + A . (B’ + B)= B . 1 + A . 1 = B + A = (A + B)Logic Circuit:Y = (A + B)Canonical Sum-of-Products FormIf each product term is a minterm, then the expression is said to be in a canonical sum-of-products formor standard SOP form.Example:Y = A’ . B + A . B’ + A . B (canonical SOP form)Y = A + B (simplified form)3 Variable Example:Y = A’ . B . C + A . B’ . C + A . B . C’ + A . B . C= F(A, B, C)Simplification= Σ m(3, 5, 6, 7)Y = A’ . B . C + A . B’ . C + A . B . C’ + A . B . CY = B . C . (A’ + A) + A . C .(B’ + B) + A . B . (C’ + C) using Adjacency Theorem= B . C. 1 + A . C . 1 + A . B . 1= B . C + A . C + A . BY = A . B + A . C + B . CB. S. Umashankar, BNMITPage 4www.bookspar.com | VTU NOTES | QUESTION PAPERS | NEWS | RESULTS | FORUMS

www.bookspar.com | VTU NOTES | QUESTION PAPERS | NEWS | RESULTS | FORUMS10CS 33 LOGIC DESIGNExample: Consider a two-variable truth table as given below:UNIT – 2 Combinational Logic CircuitsInputsOutputA B f0 0 00 1 11 0 11 1 1The two-variable K-map is drawn as shown below:TerminologyLiteralA given product term consists of some number of variables, each of which may be in uncomplementedor complemented form. Each appearance of a variable, either in uncomplemented or complemented, iscalled a literal.Example: The product term AB’C has 3 literals, and the term A’BC’D has 4 literalsImplicantA product term that indicates the input valuation for which a given function is equal to 1 is called animplicant of the function. Also there are the implicants that correspond to all possible pairs of mintermsthat can be combined (set of 2 i minterms, i