Benha University Time : 3 Hrs
Benha High Institute of Technology Department : Electrical Engineering
Jan 2011 – Fall semester Course name : E211 Digital Logic Circuit
Exam (Regular), Year : 2nd
Time Allowed: Hours
Attempt all questions
Q1) (12 points)
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If the state of a 12 bit register is 1010 1101 1100. What is its content if it represents
(1)-Three decimal digits in BCD (2)- Three decimal digits in excess-3 code.
(3)-Three decimal digits in 84-2-1 (4)- A decimal number
*Answer*
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XXX
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7X9
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6XX
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2780 whereX is invalid Code For Decimal Digits
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List the numbers from 10 to 26 in base 12.
*Answer*
A, B, 10,11,12,13,,14,15,`16,17,18,19,1A,1B,20,21,22
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Assume a 3- input AND gate with output F and a 3- input OR gate with output G. The inputs are A, B, and C. show the signals by means of timing diagram of the outputs F and G as function of the 3 inputs ABC (use all 8 possible ABC combinations).
A
B
C
F
G
Q2) (12 points)
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List the truth table of the function
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*Answer*
F= xy + xy\ + y\z =Σ(1,4,5,6,7)
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Y
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F
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0
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0
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0
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0
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0
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1
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1
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0
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1
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0
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0
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0
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1
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1
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0
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1
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0
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0
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1
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1
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0
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1
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1
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1
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1
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0
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1
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1
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1
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1
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1
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1
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1
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1
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1
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1
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Express the Complement of the following functions in sum of minterms.
F1(A,B,C,D) = Σ(0,2,6,11,13,14) , F2(x,y,z)= П(0,3,6,7)
*Answer*
F1\ = Σ(1,3,4,5,7,8,9,10,12,15) F2\ = Σ( 0,3,6,7)
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show that the dual of a Two input XOR is equal to its complement
*Answer*
XOR= XY\ + X\Y
Complement = (XY\ + X\Y)\= (XY\)\ (X\Y)\ = (X\ +Y)( X + Y\)= X\ X + Y Y\ + xy + x\y\= xy+x\y\=XNOR------ 1
Dual = (x+y\)(x\+y)=xx\+xy+x\y\+yy\=xy+x\y\=XNOR----------2
1=2
Q3) (12 points)
For the function F (A,B,C,D) = Σ (0,1,2,3,4,8,9,12)
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Simplify the function with the suitable map.
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Implement the function with two level AND- OR gates
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Implement the function with two level NAND gates.
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Implement the function with two level NOR- OR.
1
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1
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1
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1
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1
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*Answer*
F= A\B\ + C\D\ + B\C\
Q4) (16 points)
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For circuit that operate as a Full Adder, construct a truth table, simplify the function obtained by the truth table, and implement the simplified function with suitable gates.
*Answer*
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X
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S
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C
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0
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1
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0
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1
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1
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1
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1
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1
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Repeat the above item for code conversion circuit that converts from BCD code into excess-3 code, taking the unused combinations as Don’t Care conditions.
Q5) (8 points)
Analyze the given circuit below to obtain the logic function for F1 & F2.
*Answer*
F1= T2 + T3
T1 = (A+B +C)\ = A\B\C\
T2 = ABC
F2 = AB + AC + (BC)\ = AB + AC + B\ + C\ ------------------------1
F2\ = (AB)\(AC)\(BC)
T3 = T1.F2\ = (A\B\C\)(AB)\(AC)\(BC)
F1 = T2 + T3 = ABC + (A\B\C\)(AB)\(AC)\(BC)--------------------2
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