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 that decoders have active low outputs.
. Build your circuit and test it.
. Demonstrate the operation of the circuit to your instructor.
Multiplexer
. From the truth table in decoder section, pick out the terms needed for
output.
. Use select and input lines of multiplexer to connect appropriate logic.
. Build your circuit and test it.
. Demonstrate the operation of the circuit to your instructor.
Multiplexer Example Implement the following Boolean function using a 4x1 Mux;
Build the Boolean function F(W, X, Y, Z) = ∑ (1,3,4,11,12,13,14,15) using a) a 8x1 multiplexer and external gates. b) a 4x1 multiplexer and external gates. c) two 3-to-8 decoders with enables and external gates with a maximum of 4 inputs.
(a) Implement the following Boolean functions using decoders. i) F1 = x'y z' + x Z ii) F2 = x y' z' + x' y (b) Implement the following Boolean function using multiplexers. i) F1 (a, b, c, d) = Σ(1, 3, 4, 11, 12, 13, 14, 15) ii) F2 (a, b, c, d)= Σ(1, 2, 5, 7, 8, 10, 11, 13, 15)
A multiplexer (MUX) is a logic function that combines several inputs and a control input, the output of which is one of the inputs selected by the control input. A2-1 MUX is shown below: Where X and Y are inputs and S is the control input. The Truth Table of the 2-1 MUX is given by: Show that the 2-1 MUX forms a complete set of logic functions by realizing a NOR gate using only 2-1 MUXes.
7. (24 pts.) Implement the following Boolean function with an 8-to-1 multiplexer, a 2-to-4-line decoder, 3 x inverters and a OR-gate. (20 pts.) F(A, B, C, D, E) -2 (0,1,2,3,5,6,7,8,9,10,13,14,16,19,23,24) 7. (24 pts.) Implement the following Boolean function with an 8-to-1 multiplexer, a 2-to-4-line decoder, 3 x inverters and a OR-gate. (20 pts.) F(A, B, C, D, E) -2 (0,1,2,3,5,6,7,8,9,10,13,14,16,19,23,24)
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.
Question 2: Combinational Logic (15 points) Implement the following Boolean function Z(A,B,C,D) = {(1,2,5,7,8,10,11,13,15) 2.1 (5 points) Write the truth table for Z. 2.2 (5 points) Implement Z using a single 16:1 multiplexer. Make sure that you mark all inputs and outputs clearly. 2.3 (5 points) Implement Z using an 8:1 multiplexer and all necessary gates. Make sure that you mark all inputs and outputs clearly.
We are interested in designing a circuit that implements the following three Boolean functions: 3. h(x,y,z)=Σm(1,4,6) f1x,y,z)- > m(1,4,6) y-m35) (x,y, z) Σ m (2,4,6,7) 左 You are supposed to implement the circuit with a decoder constructed with NAND gates (a) [12pt] Start by drawing the block diagram of a NAND-based decoder with three inputs (x,y,z), labelling all the outputs with their corresponding Boolean functions (b) [8pt) Using a new block diagram of the NAND-based decoder, implement the circuit using...
2. Boolean Logic 2.1. Demonstrate the following identity by means of algebraic manipulations. !(x+y)z+x!y y (x+z) (last resort: use truth table) 2.2. Create the truth table and the circuit for the function F(xy,z) (x+y) (!x+z)
2. [15pt] Implement the following Boolean function using a multiplexer. f(xy.zw) m(0,2,5,8,10,14.15) Carefully label all the inputs and outputs of your multiplexer and justify your design.
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14)...