Implement B(x,y,z) = y’z + x’y’z’ + xz using a 2^3x 1 multiplexer.
Implement the function F (x,y,z)= (not x)(not z)+ xy using a. One 4-to-1 multiplexer and any additional inverters. Show your truth-table and justify your choice of select inputs. b. One 2-to-1 multiplexer and the minimal number of gates. Show the truth table used to derive your circuit.
Multiplexer Example Implement the following Boolean function using a 4x1 Mux; F(x,y,z) = Σ (1,2,6,7) Decoder Example Implement the following functions for a full adder using decoder; S(x,y,z) = Σ (1,2,4,7) C(x,y,z) = Σ (3,5,6,7) Implement the following Boolean function; F(x,y,z) = Σ (0,2,3,7): Using; 1. Two 2x4 decoders and logic gates 2. One 4x1 multiplexer Decoder . Draw the truth table for the function to be implemented. . Pick the terms for output. . Derive appropriate logic to combine terms. . Use two 2x4 decoders to make one3x8 decoder. . Pay attention to fact...
Design a 6 to 1 multiplexer (inputs A,B,C,D,E,F,S[2:0] and output Z) (a) Implement the 6 to 1 multiplexer using only CMOS NORs, NANDs and inverters. ( b) Implement the 6 to 1 multiplexer using only CMOS transmission gates and inverters. (c) Which approach is better and why?
Realizing the following functions using only 8-to-1 multiplexer: F_1(x, y, z) = Sigma m(0, 2, 3, 5, 7) F-(x, y, z)=y' + z
Question #6 6 points Implement the function from the truth table below (X, Y, Z are inputs. F is the output) using a) An 8:1 multiplexer b) A 4:1 multiplexer and one inverter c) A 2:1 multiplexer and two other logic gates Y z F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 -
17. For f(x, y)=e***+y)? of Ox? XZ of 18. For f(x, y, z)= =? y + z oz 19. For f(x, y, z) = cos’ (3x – y’) – x’ tanz, ar ax of = ? 20. For S(x, y) = x cos y + ye", дхду
If x, y, and z ∈ Z show that (x + y)z = xz + yz, where x = (a, b), y = (c, d), and z = (e, f)
I. a) (4 points) For a given function F(x, y, z) = xz + (y + z)(x + z) Draw the logic circuit diagram of the function: b) Using Boolean Algebra to simply the above function c) Use Demorgan's Theorem to find out the complement of the above function F(x,y,z)xz+ + 2)(x +z)
6. Given F(x,y,z) = x'yz + xz (20 points) 1) Express F as a sum of minterms using algebraic manipulation. (5 points) F(x, y, z)= (x'y + 2) Draw the truth table for F (5 points) 3) Implement the original function F using 2-input gates. (5 points) 4) Simplify Fusing algebraic mplify F using algebraic manipulation. (5 points)
Digital logic design
Question 2 [4+6=10Marks] I. Implement following function using 16 x 1 multiplexer? F(A,B,C,D) = I l.ec.(D1, D2, D3, D4,10,11,13,15) II. Implement function F given above using 8 x 1 multiplexer?