# EEL3705 TPS QUIZZES Quiz 2 1 Use a

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EEL-3705 TPS QUIZZES

Quiz 2 -1

Use a Venn Diagram to show

Use a Venn Diagram to show

Quiz 2 -2

Prove the following using a Venn Diagram

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

Solution

Quiz 2 -5

Prove the following using Switching Algebra

Prove the following using Switching Algebra

Quiz 2 -6

Problem Given Use Demorgan’s Thm to find

Solution Find Use De. Morgan’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

Use a Venn Diagram to show

Quiz 2 -9

Problem Use a Truth Table to evaluate

Solution A B C F 0 0 0 1 0 1 1 0 1 1 1

Quiz 2 -10

Problem Use a Truth Table to evaluate

Solution A B C F 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1

Quiz 2 -11

Problem Expand the following function represent F in truth table form

Solution

Solution A B C F 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1

Quiz 2 -12

Problem Expand the following function represent F in truth table form

Solution

Solution A B C F 0 0 0 1 0 1 1 0 0 1 1 1 1 0

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 A B C F 0 0 0 1 0 1 1 0 1 1 1

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 A B C F 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1

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 A B C F 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1

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 Truth Table A B Y 0 0 0 1 0 1 0 0 1 1 1 0

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 AND NOT OR

Solution

Quiz 2 -20

Problem Show that this circuit implements the expression

Solution P 1

Solution A B C F*=(ab)’ F=(F*c)’ ab+c’ 0 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1

Quiz 2 -21

Problem Find a simplified logic expression and network for this logic circuit? Use a truth table to verify your results

Solution P 2 P 1 P 3

Solution

Verification A B C P 2 P 3 Fo Fs 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0

Quiz 2 -22

Problem Find a simplified logic expression and network for this logic circuit? Use a truth table to verify your results

Solution P 1 P 2 P 3 P 4

Solution P 1 P 2 P 3 P 4

Solution

Verification A B C P 3 P 4 Fo Fs 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1

Solution

Quiz 2 -22

Problem • Design a circuit which implements the function y=2 x+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 Let’s “precompute” Y. X 1 X 0 X Y 0 0 0 1 1 3 1 0 2 5 1 1 3 7 y=2 x+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) = log 2(8) = 3 bits to represent Y

Solution Use a three bit unsigned output vector for y. X 1 X 0 X Y Y 2 Y 1 Y 0 0 1 1 3 0 1 1 1 0 2 5 1 0 1 1 1 3 7 1 1 1 By Inspection:

Solution Circuit Simulation

Quiz 2 -23

Problem • Design a circuit which implements the function y=2 x-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 Let’s “precompute” Y. X 1 X 0 X Y 0 0 0 -1 0 1 1 0 2 3 1 1 3 5 y=2 x-1

Solution Bits needed for Y Ylow = -1 Yhigh = 5 Need the largest in magnitude 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+log 2(max(5, 1)+1)=1+log 2(6)=3. 58 = 4 bits to represent Y

Solution Use a four bit signed output vector for y. X 1 X 0 Y Y 3 Y 2 Y 1 Y 0 0 0 -1 1 1 0 0 0 1 1 0 3 0 0 1 1 5 0 1 By Inspection:

Solution Circuit Simulation

Quiz 2 -24

Problem • Design a circuit which implements the function y=2 x-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 Let’s “precompute” Y. X 1 X 0 X Y 0 0 0 -1 0 1 1 0 -2 -5 1 1 -1 -3 y=2 x-1

Solution Bits needed for Y Ylow = -5 Yhigh = 1 Need the largest in magnitude 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+log 2(6)=3. 58 = 4 bits to represent Y

Solution Use a three bit unsigned output vector for y. X 1 X 0 X Y Y 3 Y 2 Y 1 Y 0 0 -1 1 1 0 0 0 1 1 0 -2 -5 1 0 1 1 -1 -3 1 1 0 1 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 Truth Table X 2 X 1 X 0 F 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1

Solution