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(06) Proof the following absorption theorem using the fundamental of Boolean algebra X+ XY= X (07) Use De Morgan's Theorem, to find the complement of the following function F(X, Y, Z) = XYZ + xyz (08) Obtain the truth table of the following function, then express it in sum-of-minterms and product-of-maxterms form F= XY+XZ (Q9) For the following abbreviated forms, find the corresponding canonical representations, (a) F(A, B, C) = (0,2,4,6) (b) F(X, Y, Z) = II (1,3,5,7)
a. Design a circuit for your 3 bedroom house that will turn on a green light in your bedroom when an intruder enters your house through the window of your front door. b. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step. F(x,y,z) = x’y + xyz’ + xyz F(w,x,y,z) =(xy’+w’z))(wx’+yz’) c. Construct a truth table for the following xyz + x(yz)’+(xyz)’ b. (x+y)(x+z)(x’+z)
1. (15 pts) Simplify the following Boolean functions using K-maps: a. F(x,y,z) = (1,4,5,6,7) b. F(x, y, z) = (xy + xyz + xyz c. F(A,B,C,D) = 20,2,4,5,6,7,8,10,13,15) d. F(A,B,C,D) = A'B'C'D' + AB'C + B'CD' + ABCD' + BC'D e. F(A,B,C,D,E) = (0,1,4,5,16,17,21,25,29) 2. (12 pts) Consider the combinational logic circuit below and answer the following: a. Derive the Boolean expressions for Fi and F2 as functions of A, B, C, and D. b. List the complete truth table...