DEPARTMENT OF
INFORMATION TECHNOLOGY
Sub
Name :
CS1202-Digital Principles and System Design
Branch/Sem
: IT / III
CS1202 Digital
Principles and System Design
Question
Bank
Unit – I
Boolean algebra and Logic Gates
Part A
1. Find the
hexadecimal equivalent of the decimal number 256
2. Find the octal
equivalent of the decimal number 64
3. What is meant
by weighted and non-weighted coding?
4. Convert A3BH
and 2F3H into binary and octal respectively
5. Find the
decimal equivalent of (123)9
6. Find the octal
equivalent of the hexadecimal number AB.CD
7. Encode the ten
decimal digits in the 2 out of 5 code
8. Show that the
Excess – 3 code is self –complementing
9. Find the
hexadecimal equivalent of the octal number 153.4
10. Find the
decimal equivalent of (346)7
11. A hexadecimal
counter capable of counting up to at least (10,000)10 is to be
constructed.
What is the
minimum number of hexadecimal digits that the counter must have?
12. Convert the
decimal number 214 to hexadecimal
13. Convert 231.3
4 to base 7
14. Give an
example of a switching function that contains only cyclic prime implicant
15. Give an
example of a switching function that for which the MSP from is not unique.
16. Express x+yz
as the sum of minterms
17. What is prime
implicant?
18. Find the
value of X = A B C (A+D) if A=0; B=1; C=1 and D=1
19. What are
‘minterms’ and ‘maxterms’?
20. State and
prove Demorgan’s theorem
21. Find the
complement of x+yz
22. Define the
following : minterm and term
23. State and
prove Consensus theorem
24. What theorem
is used when two terms in adjacent squares of K map are combined?
25. How will you
use a 4 input NAND gate as a 2 input NAND gate?
26. How will you
use a 4 input NOR gate as a 2 input NOR gate?
27. Show that the
NAND connection is not associative
28. What happens
when all the gates is a two level AND-OR gate network are replaced by
NOR gates?
29. What is meant
by multilevel gates networks?
30. Show that the
NAND gate is a universal building block
31. Show that a
positive logic NAND gate is the same as a negative logic NOT gate
32. Distinguish
between positive logic and negative logic
33. Implement AND
gate and OR gate using NAND gate
34. What is the
exact number of bytes in a system that contains (a) 32K byte, (b) 64M bytes,
and (c) 6.4G
byte?
35. List the
truth table of the function:
F = x y + x y’ +
y ’z
Part B
1. (a) Explain
how you will construct an (n+1) bit Gray code from an n bit
Gray code
(b) Show that the
Excess – 3 code is self -complementing
2. (a) Prove that
(x1+x2).(x1’. x3’+x3) (x2’ + x1.x3) =x1’x2
(b) Simplify
using K-map to obtain a minimum POS expression:
(A’ + B’+C+D)
(A+B’+C+D) (A+B+C+D’) (A+B+C’+D’) (A’+B+C’+D’)
(A+B+C’+D)
3. Reduce the
following equation using Quine McClucky method of
minimization F
(A,B,C,D) = _m(0,1,3,4,5,7,10,13,14,15)
4. (a) State and
Prove idempotent laws of Boolean algebra.
(b) using a K-Map
,Find the MSP from of F= _(0,4,8,12,3,7,11,15) +_d(5)
5 (a) With the
help of a suitable example ,explain the meaning of an redundant prime i
implicant
(b) Using a
K-Map, Find the MSP form of F= _ (0-3, 12-15) + _d (7, 11)
6 (a) Simplify
the following using the Quine – McClusky minimization technique
D = f(a,b,c,d) = _
(0,1,2,3,6,7,8,9,14,15).Does
Quine –McClusky take care of don’t
care conditions?
In the above problem, will you consider any don’t care conditions?
Justify your
answer
(b) List also the
prime implicants and essential prime implicants for the above case
7 (a) Determine
the MSP and MPS focus of F= _ (0, 2, 6, 8, 10,
12, 14, 15)
(b) State and
Prove Demorgan’s theorem
8 Determine the
MSP form of the Switching function
F = _
(
0,1,4,5,6,11,14,15,16,17,20- 22,30,32,33,36,37,48,49,52,53,56,63)
9. (a) Determine
the MSP form of the Switching function
F( a,b,c,d) =_(0,2,4,6,8) + _d(10,11,12,13,14,15)
(b) Find the
Minterm expansion of f(a,b,c,d) = a’(b’+d) + acd’
10 Simplify the
following Boolean function by using the Tabulation Method
F= _
(0,
1, 2, 8, 10, 11, 14, 15)
11 State and
Prove the postulates of Boolean algebra
12 (a) Find a Min
SOP and Min POS for f = b’c’d + bcd + acd’ + a’b’c + a’bc’d
13 Find an
expression for the following function usingQuine McCluscky method
F= _
(0,
2, 3,5,7,9,11,13,14,16,18,24,26,28,30)
14 State and
Prove the theorems of Boolean algebra with illustration
15 Find the MSP
representation for
F(A,B,C,D,E) = _m(1,4,6,10,20,22,24,26)
+ _d
(0,11,16,27) using K-Map method
Draw the circuit
of the minimal expression using only NAND gates
16 (a) Show that
if all the gates in a two – level AND-OR gate networks are replaced by
NAND gates the
output function does not change
(b) Why does a
good logic designer minimize the use of NOT gates?
17 Simplify the
Boolean function F(A,B,C,D) = _ m (1,3,7,11,15) +
_d
(0,2,5) .if don’t
care conditions
are not taken care, What is the simplified Boolean function .What are
your comments on
it? Implement both circuits
18 (a) Show that
if all the gate in a two – level OR-AND gate network are replaced by NOR
gate, the output
function does not change.
(b) Implement Y =
(A+C) (A+D’) ( A+B+C’) using NOR gates only
19 (a) F3 =
f(a,b,c,d) = _ (2,4,5,6)
F2 = f(a,b,c,d) =
_ (2,3,,6,7)
F1 = f(a,b,c,d) =
_ (2,5,6,7)
.Implement the above Boolean functions
(i) When each is
treated separately and
(ii)When sharing
common term
(b) Convert a NOR
with an equivalent AND gate
20 Implement the
Switching function whose octal designation is 274 using NAND gates only
21 Implement the
Switching function whose octal designation is 274 using NOR gates only
22 (a) Show that
the NAND operation is not distributive over the AND operation
(b) Find a
network of AND and OR gate to realize f(a,b,c,d) = _
m
(1,5,6,10,13,14)
23 What is the
advantages of using tabulation method? Determine the prime implicants of the
following
function using tabulation method
F( W,X,Y,Z) = _(1,4,6,7,8,9,10,11,15)
23 (a) Explain
about common postulates used to formulates various algebraic structures
(b) Given the
following Boolean function F= A”C + A’B + AB’C + BC
Express it in sum
of minterms & Find the minimal SOP expression
Unit –
II Combinational Logic
Part A
1. How will you
build a full adder using 2 half adders and an OR gate?
2. Implement the
switching function Y= BC’ + A’B + D
3. Draw 4 bit
binary parallel adder
4. Write down the
truth table of a full adder
5. Write down the
truth table of a full sub tractor
6. Write down the
truth table of a half sub tractor
7. Find the
syntax errors in the following declarations (note that names for primitive
gates
are optional):
module Exmp1-3(A,
B, C, D, F)
inputs A,B,C,
and g1(A,B,D);
not (D,B,A);
OR (F,B,C);
endmodule ;
8. Draw the logic
diagram of the digital circuit specified by
module circt
(A,B,C,D,F);
input A,B,C,D;
output F;
wire w,x,y,z,a,d;
and (x,B,C,d);
and y,a,C);
and (w,z,B);
or (z,y,A);
or (F,x,w);
not (a,A);
not (d,D);
endmodule
9. Define
Combinational circuits
10. Define Half
and Full adder
11. Give the four
elementary operations for addition and subtraction
12. Design the
combinational circuit with 3 inputs and 1 output. The output is 1 when the
binary value of
the inputs is less than 3.The output is 0 otherwise
13. Define HDL
14. What do you
mean by carry propagation delay?
15. What is code
converter?
16. Give short
notes on Logic simulation and Logic synthesis
17. What do you
mean by functional and timing simulation?
18. What do you
mean by test bench?
19. Give short
notes on simulation versus synthesis
20. Define half
sub tractor and full sub tractor
Part B
1 Design a 4 bit
magnitude comparator to compare two 4 bit number
2 Construct a
combinational circuit to convert given binary coded decimal number into an
Excess 3 code for
example when the input to the gate is 0110 then the circuit should
generate output
as 1001
3 Design a
combinational logic circuit whose outputs are F1 = a’bc + ab’c and
F2 = a’ + b’c +
bc’
4 (a) Draw the
logic diagram of a *-bit 7483 adder
(b) Using a
single 7483, Draw the logic diagram of a 4 bit adder/sub tractor
5 (a) Draw a
diode ROM, which translates from BCD 8421 to Excess 3 code
(b) Distinguish
between Boolean addition and Binary addition
6 Realize a BCD
to Excess 3 code conversion circuit starting from its truth table
7 (a) Design a
full sub tractor
(b) How to it
differ from a full sub tractor
8 Design a
combinational circuit which accepts 3 bit binary number and converts its
equivalent excess
3 codes
9 Derive the
simplest possible expression for driving segment “a” through ‘g’ in an 8421
BCD to seven
segment decoder for decimal digits 0 through 9 .Output should be
active high
(Decimal 6 should be displayed as 6 and decimal 9 as 9)
10 Write the HDL
description of the circuit specified by the following Boolean function
(i) Y= (A+B+C)
(A’+B’+C’)
(ii) F= (AB’ +
A’B) (CD’+C’D)
(iii) Z = ABC +
AB’ + A(D+B)
(iv) T= [(A+B}
{B’+C’+D’)]
11 Design 16 bit
adder using 4 7483 ICs
Unit –
III Design with MSI Devices
Part A
1. What is a
decoder and obtain the relation between the number of inputs ‘n’ and outputs
‘m’ of a decoder?
2. Distinguish
between a decoder and a demultiplexer
3. Using a single
IC 7485 ; draw the logic diagram of a 4 bit comparator
4. what is
decoder
5. What do you
mean by encoder?
6. Write the
short notes on priority encoder
7. What is
multiplexer? Draw the logic diagram of8 to 1 line multiplexer
8. What do you
mean by comparator?
9. Write the HDL
description of the circuit specified by the following Boolean function
X=AB+ACD+BC’
10. How does ROM
retain information?
11. Distinguish
between PAL and PLA
12. Give the
classification of memory
13. What is
refreshing? How it is done?
14. What is
Hamming code?
15. Write a short
notes on memory decoding
16. List the
basic types of programmable logic devices
17. What is PAL?
How it differ from PROM and PLA?
18. Write a short
notes on – PROM,EPROM,EEPROM
19. How many
parity bits are required to form Hamming code if massage bits are 6?
20. How to find
the location of parity bits in the Hamming code?
21. Generate the
even parity Hamming codes for the following binary data
1101, 1001
22. A seven bit
Hamming code is received as 11111101. What is the correct code?
23. Compare
static RAMs and dynamic RAMs
24. Define
Priority encoder
25. Define PLDs
Part B
1. Implement the
switching function F= _(0,1,3,4,7) using a 4 input MUX and
explain
2. Explain how
will build a 64 input MUX using nine 8 input MUXs
3. State the
advantages of complex MSI devices over SSI gates
4. Implement the
switching function F(A,B,C) = _ ( ,2,4,5) using
the DEMUX 74156
5. Implement the
switching function F= _(0,1,3,4,12,14,15) using an 8 input MUX
6. Explain how
will build a 16 input MUX using only 4 input MUXs
7. Explain the
operation of 4 to 10 line decoder with necessary logic diagram
8. Draw a neat sketch
showing implementation of Z1 = ab’d’e + a’b’c’e’ + bc + de ,
Z2 = a’c’e, Z3 =
bc +de+c’d’e’+bd and Z4 = a’c’e +ce using a 5*8*4 PLA
9. Implement the
switching functions:
Z1 = ab’d’e +
a’b’c’e’ + bc + de ,
Z2 = a’c’e,
Z3 = bc
+de+c’d’e’+bd and
Z4 = a’c’e +ce
Using a 5*8*4 PLA
10 Design a
switching circuit that converts a 4 bit binary code into a 4 bit Gray code
using
ROM array
11.Design a
combinational circuit using a ROM ,that accepts a 3- bit number and
generates an
output binary number equal to the square of the given input number
Unit –
IV Synchronous Sequential Logic
Part A
1. Derive the
characteristic equation of a D flip flop
2. Distinguish
between combinational and sequential logic circuits
3. What are the
various types of triggering of flip-flops?
4. Derive the
characteristic equation of a T flip flop
5. Derive the
characteristic equation of a SR flip flop
6. What is race
round condition? How it is avoided?
7. List the
functions of asynchronous inputs
8. Define Master
slave flip flop
9. Draw the state
diagram of ‘T’ FF, ‘D’ FF
10. Define
Counter
11. What is the
primary disadvantage of an asynchronous counter?
12. How
synchronous counters differ from asynchronous counters?
13. Write a short
note on counter applications
14. Compare Moore and Mealy models
15. When is a
counter said to suffer from lock out?
16. What is the
minimum number of flip flops needed to build a counter of modulus z 8?
17. State the
relative merits of series and parallel counters
18. What are
Mealy and Moore
machines?
19. When is a
counter said to suffer from lockout?
20. What is the
difference between a Mealy machine and a Moore Machines?
21. Distinguish
between synchronous and asynchronous sequential logic circuits
22. Derive the
characteristic equation of a JK flip flop
23. How will you
convert a JK flip flop into a D flip flop
24. What is mean
by the term ‘edge triggered’?
25. What are the
principle differences between synchronous and asynchronous networks
26. What is
lockout? How it is avoided?
27. What is the
pulse mode operation of asynchronous sequential logic circuits not very
popular?
28. What are the
advantages of shift registers?
29. What are the
applications of a shift register?
30. How many flip
–flops are needed to build an 8 bit shift register?
31. A shift
register comprises of JK flip-flops. How will you complement of the counters of
the
register
32. List the
basic types of shift registers in terms of data movement.
33. Write a short
notes on PRBS generator
34. Give the HDL
dataflow description for T flip - flop
35. Give the HDL
dataflow description for JK flip – flop
Part B
1 Draw the state
diagram and characteristics equation of T FF, D FF and JK FF
2 (a) What is
race around condition? How is it avoided?
(b) Draw the
schematic diagram of Master slave JK FF and input and output
waveforms.Discuss
how it prevents race around condition
3 Explain the
operation of JK and clocked JK flip-flops with suitable diagrams
4 Draw the state
diagram of a JK flip- flop and D flip – flop
5 Design and
explain the working of a synchronous mod – 3 counter
6 Design and
explain the working of a synchronous mod – 7 counter
7 Design a
synchronous counter with states 0,1, 2,3,0,1 …………. Using JK FF
8 Using SR flip
flops, design a parallel counter which counts in the sequence
000,111,101,110,001,010,000
………….
9 Using JK flip
flops, design a parallel counter which counts in the sequence
000,111,101,110,001,010,000
………….
10 (a) Discuss a
decade counter and its working principle
(b) Draw as
asynchronous 4 bit up-down counter and explain its working
11 (a) How is the
design of combinational and sequential logic circuits possible with PLA?
(b) Mention the
two models in a sequential circuit and distinguish between them
12 Design a
modulo 5 synchronous counter using JK FF and implement it. Construct its
timing diagram
12 A sequential
machine has one input line where 0’s and 1’s are being incident. The
machine has to
produce a output of 1 only when exactly two 0’s are followed by a ‘1’
or exactly two
1’s are followed by a ‘0’.Using any state assignment and JK
flipflop,synthesize
the machine
13 Using D flip
–flop ,design a synchronous counter which counts in the sequence
000, 001, 010,
011, 100, 1001,110,111,000
15 Using JK
flip-flops, design a synchronous sequential circuit having one and one
output. the
output of the circuit is a 1 whenever three consecutive 1’s are
observed.
Otherwise the output is zero
14 Design a
binary counter using T flip – flops to count in the following sequences:
(i)
000,001,010,011,100,101,110,111,000
(ii)
000,100,111,010,011,000
15 (a) Design a
synchronous binary counter using T flip – flops
(b) Derive the
state table of a serial binary adder
17. Design a 3
bit binary Up-Down counter
18. (i) Summarize
the design procedure for synchronous sequential circuit
(ii) Reduce the
following state diagram
Unit – V
Asynchronous Sequential Logic
Part A
1. Distinguish
between fundamental mode and pulse mode operation of asynchronous
sequential
circuits
2. What is meant
by Race?
3. What is meant
by critical race?
0/0
a
b
c
d
e
g
f
0/0
0/0
1/1
1/1
0/0
1/1
1/1
0/0
1/0
0/0
1/
0
4. What is meant
by race condition in digital circuit?
5. Define the
critical rate and non critical rate
6. What are races
and cycles?
7. What is the
significance of state assignment?
8. What are the
steps for the analysis of asynchronous sequential circuit?
9. What are the
steps for the design of asynchronous sequential circuit?
10. Write short
notes on (a) Shared row state assignment
(b) One hot state
assignment
11. What are
Hazards?
12. What is a
static 1 hazard?
13. What is a
static 0 hazard?
14. What is
dynamic hazard?
15. Define static
1 hazard, static 0 hazards, and dynamic hazard?
16. Describe how
to detect and eliminate hazards from an asynchronous network?
17. What is
static hazard?
18. List the
types of hazards?
19. How to
eliminate the hazard?
20. Draw the wave
forms showing static 1 hazard?
Part B
1. What is the
objective of state assignment in asynchronous circuit? Give hazard – free
realization for
the following Boolean function f(A,B,C,D) = _M(0,2,6,7,8,10,12)
2. Summarize the
design procedure for asynchronous sequential circuit
a. Discuss on
Hazards and races
b. What do you
know on hardware descriptive languages?
3. Design an
asynchronous sequential circuit with 2 inputs X and Y and with one output Z
Wherever Y is 1,
input X is transferred to Z .When Y is 0; the output does not change for
any change in
X.Use SR latch for implementation of the circuit
4. Develop the
state diagram and primitive flow table for a logic system that has 2 inputs,x
and y and an
output z.And reduce primitive flow table. The behavior of the circuit is stated
as follows.
Initially x=y=0. Whenever x=1 and y = 0 then z=1, whenever x = 0 and y = 1
then z = 0.When
x=y=0 or x=y=1 no change in z ot remains in the previous state. The
logic system has
edge triggered inputs with out having a clock .the logic system changes
state on the
rising edges of the 2 inputs. Static input values are not to have any effect in
changing the Z
output
5. Design an
asynchronous sequential circuit with two inputs X and Y and with one output Z.
Whenever Y is 1,
input X is transferred to Z.When Y is 0,the output does not change for
any change in X.
6. Obtain the
primitive flow table for an asynchronous circuit that has two inputs x,y and
one
output Z. An
output z =1 is to occur only during the input state xy = 01 and then if the
only if
the input state
xy =01 is preceded by the input sequence.
7. A pulse mode
asynchronous machine has two inputs. It produces an output whenever two
consecutive
pulses occur on one input line only .The output remains at ‘1’ until a pulse
has
occurred on the
other input line. Draw the state table for the machine.
8.
(a) How will you
minimize the number of rows in the primitive state table of an incompletely
specified
sequential machine
(b) State the
restrictions on the pulse width in a pulse mode asynchronous sequential
machine
9. Construct the
state diagram and primitive flow table for an asynchronous network that has
two inputs and
one output. The input sequence X1X2 = 00,01,11 causes the output to
become 1.The next
input change then causes the output to return to 0.No other inputs will
produce a 1
output
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