ma2184a1 Logic
1. If p stands for it rains in Paris and q stands for we bring umbrellas, then express each of the
following in symbolic form.
(a) If it rains in Paris, then we bring our umbrellas.
(b)
ma2184a5, ma2504a5
Graphs
1. Does there exist a simple graph with five vertices of the following degrees? If so, draw such a graph.
(a) 3, 3, 3, 3, 2
(b) 1, 2, 3, 4, 5
(c) 3, 4, 3, 4, 3
(d) 0, 1, 2, 2
ma2144a2
Sets, Relations and Functions
1. For each of the following, choose an appropriate universe of discourse and a predicate to define the set
and its complement.
(a) The set of all odd integers.
MA2184/MA2504 Discrete Mathematics for Computing (08-09 sem B)
Take Home Quiz 1 (Due date: 6-3-2009)
Suggested Solutions:
1. a) x(B (x) F (x)
b) xy [(B (x) F (x) (M (y ) T (x, y )]
c) x[B (x) y (M (y
EE 2000 Logic Circuit Design
Semester B 2016/17
Tutorial 9
1.
Reduce the number of states in the following state table by implication table method and
show a new state table with states elimination.
N
EE 2000 Logic Circuit Design
Semester B 2016/17
Tutorial 10
1.
Using JK FFs and with the minimum number of states to design a counter with
counting sequence: 0,4,2,1,6 and repeat. State whether the ci
EE 2000 Logic Circuit Design
Semester A 2016 B
Tutorial 4
1.
Consider a 4-variable Boolean function. Using K-map, list the cells adjacent to cell m13.
2.
Plot the following functions on the K-map.
(a)
EE 2000 Logic Circuit Design
Semester A 2016B
Tutorial 1
1. (a) Convert (110011.011)2 to decimal and octal forms.
(b) Convert (38.75)10 to binary and hexadecimal forms.
(c) Complete the following tabl
EE 2000 Logic Circuit Design
Semester B 2016
Tutorial 8
1.
Construct a 4 x 16 decoder (with enable input) using five 2 x 4 decoder (with enable input)
modules. Show the schematic diagram neatly.
2.
Ho
EE 2000 Logic Circuit Design
Semester A 2016B
Tutorial 6
1.
(i) Draw the truth table for a half adder.
(ii) Design a half adder using NOR gates only.
2.
With the following functions, design a circuit
EE 2000 Logic Circuit Design
Semester A 2016B
Tutorial 5
1.
Design a combinational circuit for a 3-bit Binary-to-Gray code converter.
2.
(i) Complete the truth table of the following circuit given in
MA2184/MA2504 Discrete Mathematics for Computing (08-09 sem B)
Take Home Quiz 1 (Due date: 6-3-2009)
1. Let F (x) be the predicate x is a freshman, M (y ) be the predicate y is a math course, B (x) be
MA2184/MA2504 Discrete Mathematics for Computing (08-09 sem B)
Take Home Quiz 2 (Due date: 17-4-2009)
Suggested Solutions:
1. a) Since each element in A can map to any elements in B , so each of them
ma2184a1, ma2504a1
Logic
1. If p stands for it rains in Paris and q stands for we bring umbrellas, then express each of the
following in symbolic form
(a) if it rains in Paris, then we bring our umbre
ma2184a3, ma2504a3
Combinatorics
1. Using pigeon hole principal show that in any gathering of six people there are either three people who all
know each other or three people none of whom knows either
ma2184a2
Sets, Relations and Functions
1. For each of the following, choose an appropriate universe of discourse and a predicate to define the set
and its complement.
(a) The set of all odd integers.
ma2184a5, ma2504a5
Graphs and Trees
1. Does there exist a simple graph with five vertices of the following degrees? If so, draw such a graph.
(a) 3, 3, 3, 3, 2
(b) 1, 2, 3, 4, 5
(c) 3, 4, 3, 4, 3
(d)
ma2184a3, ma2504a3
Combinatorics
1. Using pigeon hole principal show that in any gathering of six people there are either three people who all
know each other or three people none of whom knows either
We will now discuss generating functions, which have been widely used. The idea behind the method is very
simple. Given a sequence, we aim to find a function, called the generating function of the seq
Euler Paths
Question: Is it possible to start at some location in the town and travel across all the
bridges without crossing any bridge twice, and return to the starting point?
This is equivalent to
A binary relation R on A is an equivalence relation if R is reflexive, symmetric and
transitive. An equivalence relation provides a means of treating the members of a set
according to their properties
MA2184/MA2504 Discrete Mathematics for Computing (08-09 sem B)
Test
Suggested Solution:
1.
1
P (y )
add p
2
x(P (x) Q(x)
p
3
x(P (x) R(x)
p
4
P (y ) Q(y )
2, ui
5
P (y ) R(y )
3, ui
6
Q(y )
1, 4
7
R (
MA2184/MA2504 Discrete Mathematics for Computing (08-09 sem B)
Take Home Quiz 2 (Due date: 17-4-2009)
1. Suppose |A| = 5 and |B | = 10.
a) Find the number of functions f : A B . (Give Reason)
(10 mark
EE 2000 Logic Circuit Design
Semester B 2016
Tutorial 7
1.
An active-LOW SR latch is shown in Fig. 1, sketch the output waveform of Q based on the
inputs as shown in Fig. 1. Assume that Q starts LOW.