EEL-3705 TPS QUIZZES
Quiz 2-1
Use a Venn Diagram to show
Quiz 2-2
Prove the following using a Venn Diagram
OR
Quiz 2-3
Use a Venn Diagram to find
Use a Venn Diagram to show
Quiz 2-4
Problem Use a Venn Diagram to show Given Hint: Draw
Solution
Quiz 2-5
Prove the following using Switching Algebra
Quiz 2-6
Problem Given Use Demorgan’s Thm to find
Solution Find Use DeMorgan’s Theorem
Quiz 2-7
Problem Given Use Demorgan’s Thm to find:
Solution Given Find
Quiz 2-8
Use a Venn Diagram to show
Quiz 2-9
Problem Use a Truth Table to evaluate
Solution ABCF
Quiz 2-10
Problem Use a Truth Table to evaluate
Solution ABCF
Quiz 2-11
Problem Expand the following function represent F in truth table form
Solution
ABCF
Quiz 2-12
Problem Expand the following function represent F in truth table form
Solution
ABCF
Quiz 2-13
Problem Expand F into SOP canonical form Re-write F using the minterms notation and in a truth table.
Solution Expand F into SOP canonical form
Solution Rewrite using minterms ABCF
Quiz 2-14
Problem Expand F into POS canonical form Re-write F using only Maxterms notation and in a truth table
Solution Expand F into POS canonical form
Solution Re-write F using Maxterms and TT ABCF
Quiz 2-15
Problem Simplify F and express using SOP minterms and in a truth table
Solution Simplify F and express using SOP minterms and in a truth table
Solution Simplify F and express using SOP minterms
Solution Simplify F and express using SOP minterms
Solution ABCF
Quiz 2-16
Problem Complete the 2-input Truth Table for the following Basic Logic Gates
Solution Complete the 2-input Truth Table for the following Basic Logic Gates ABY Truth Table ABY
Quiz 2-17
Problem Given Use Demorgan’s Thm to show:
Solution 0 0
Quiz 2-18
Problem Given inputs a,b, and c, and using AND, OR, and NOT gates, Design a digital logic circuit that implements How many gates are needed for your design?
Solution
Quiz 2-19
Problem Given inputs a,b, and c, and using only NAND gates, Design a digital logic circuit that implements How many gates are needed for your design?
Solution OR AND NOT
Solution
Quiz 2-20
Problem Show that this circuit implements the expression
Solution P1
Solution ABCF*=(ab)’F=(F*c)’ab+c’
Quiz 2-21
Problem Find a simplified logic expression and network for this logic circuit? Use a truth table to verify your results
Solution P2 P3 P1
Solution
Verification ABCP2P3FoFs
Quiz 2-22
Problem Find a simplified logic expression and network for this logic circuit? Use a truth table to verify your results
Solution P2 P3 P1 P4
Solution P2 P3 P1 P4
Solution
Verification ABCP3P4FoFs
Solution
Quiz 2-22
Problem Design a circuit which implements the function y=2x+1. Let x be an unsigned 2- bit input vector. How many bits are needed to represent Y? Use a truth table to represent y. Design a logic circuit to implement the simplified logic expression for y.
Solution X1X0XY Let’s “precompute” Y. y=2x+1
Solution Bits needed for Y Ylow = 1 Yhigh = 7 Since Y is positive, we can use an unsigned binary number for Y. We need n = log 2 (Yhigh+1) = log2(8) = 3 bits to represent Y
Solution X1X0XYY2Y1Y Use a three bit unsigned output vector for y. By Inspection:
Solution Circuit Simulation
Quiz 2-23
Problem Design a circuit which implements the function y=2x-1. Let x be an unsigned 2- bit input vector. How bits are needed to represent Y? Use a truth table to represent y. Design a logic circuit to implement the simplified logic expression for y.
Solution X1X0XY Let’s “precompute” Y. y=2x-1
Solution Bits needed for Y Ylow = -1 Yhigh = 5 Since Y is negative, we will must use a signed binary number for Y. We need n = 1+log 2 (max(abs(Yhigh),abs(Ylow))+1) = 1+log2(max(5,1)+1)=1+log2(6)=3.58 = 4 bits to represent Y Need the largest in magnitude
Solution X1X0YY3Y2Y1Y Use a four bit signed output vector for y. By Inspection:
Solution Circuit Simulation
Quiz 2-24
Problem Design a circuit which implements the function y=2x-1. Let x be a signed 2-bit input vector. What is the range of y? Use a truth table to represent y. Design a logic circuit to implement the simplified logic expression for y.
Solution X1X0XY Let’s “precompute” Y. y=2x-1
Solution Bits needed for Y Ylow = -5 Yhigh = 1 Since Y is negative, we will must use a signed binary number for Y. We need 1+ log 2 (max(abs(Yhigh),abs(Ylow))+1) = 1+log2(6)=3.58 = 4 bits to represent Y Need the largest in magnitude
Solution X1X0XYY3Y2Y1Y Use a three bit unsigned output vector for y. By Inspection:
Quiz 2-25
Problem Design a circuit which accepts a three bit input vector x and produces a ‘1’ if the majority of the inputs bits are a ‘1’. That is, F=1, if number of ‘1’s’ in x is greater than number of ‘0’s’ in x. Simplify the function prior to its implementation
Solution X2X1X0F Truth Table
Solution