Download assignment 03- boolean algebra

ASSIGNMENT 03- BOOLEAN ALGEBRA
DATELINE : MONDAY 30th DECEMBER 2013
Question 1
Figure 3.1 : Logic Circuits a, b, c & d
a) Write the Boolean equation for each of the logic circuits shown in Figure 3.1
b) Create the truth table for each circuit
Question 2
Figure 3.2 : Logic Circuit
1
a) Obtain the Boolean expression of Figure 3.2 above
b) Assuming the MSB to LSB input variable arrangement as ABC develop the truth
table for outputs y1, y2 and Y.
A
Input
B
C
y1
Output
y2
Y
c) Sketch the Y output waveform timing diagram of Figure 3.2 based on the input
waveform shown in Figure 3.3 below.
Note : copy-paste Figure 3.3 to a blank document and print. Draw the Y output
timing diagram on the printed document to answer this question.
A
B
C
Y
Figure 3.3 : Question 2 Timing Diagram
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Question 3
Draw the logic circuit from the following Boolean equations and develop the truth table for
each equations.
Note : Apply Law 3 where applicable first. DO NOT simplify
a)
b)
c)
d)
e)
M = AB + (C + D)
N = (A + B + C)D
P = (AC + BC)(A + C)
Q = (A + B)BCD
S = B(A + C) + AC + AD
Question 4
Write the Boolean equation and sketch the timing diagram for outputs Y and Z from the logic
circuits in Figure 3.4
A
B
C
D
W
Z
3
Question 5
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a) Draw the logic circuit diagram for the Boolean equation above
b) Using the DeMorgan’s Theorem and Boolean Laws and Rules, simplify and reduce to
the stage where the overbars are above a single variable only
c) Draw the simplified circuit
Question 6
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Draw the logic circuit diagram for the Boolean equation as given above using :
a) Gates AND, OR and NOT only
b) Gates NAND and NOT only
c) Gates NOR and NOT only
Question 7
a) Derive the meaning and purpose of the following Boolean notation function :
i.
The  notation
ii.
The  notation
b) Write the following function in Boolean equation canonical form.
i.
F(a,b,c) = m(1,3,7)
ii.
F(a,b,c,d) = m(0,1,4,8,9,11,13)
iii. F(a,b,c) = M(1,3,7)
iv.
F(a,b,c,d) = M(3,5,6,7,8,14)
c) Given the function F below. Create the truth table and obtain the  and  notations.
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