Digital Principles and system design

1



Arulmigu Meenakshi Amman college of Engineering
Vadamavandal-604410.
Prepared by,
V.Umapathy,
Prof./Mech.


Imortant Questions and Answers
IT25202- Digital Principles and System Design
Syllabus
1. Boolean Algebra: Number Systems, Binary, Octal, Hexadecimal, Representation of
negative numbers, 1’s and 2’s Complements, Arithmetic Operations, Binary Codes. Boolean
Algebra, Theorems and Postulates, Functions, Truth Table, Logic Gates, Universal gates.
Practical:
1. Simple functions using gates
2. implementation of Boolean functions .
2. Canonical Functions: Canonical and Standard Forms, Minterms and Maxterms, Sum of
Products and Product of Sums, Conversions and Expansion.
Practical: Simplification and expansion of standard Boolean functions.
3. Karnaugh Map and Combinational Logic: Simplification of Boolean Functions, Karnaugh
Map, 2,3,4 variables, NAND / NOR Implementations, Combinational Circuits, Arithmetic
Circuits, Half and Full Adders, Subtractors. Introduction to HDL.
Practical:
1. Implementation of combinational circuits using gates for arbitrary functions.
2. Implementation of Arithmetic circuits and extended operations.
4. Combinational Logic Design: Binary Parallel adder, Carry Look-ahead Adder, BCD Adder,
Binary multiplier, Magnitude Comparator, Code Converters, Decoder, Encoder, Priority
Encoder, Mux/Demux, Applications, Introduction to HDL and HDL for these circuits.
.

Practical:
h
ec


1. Combinational circuits using code converters.
./M




2. BCD adder, encoder and decoder circuits.
of




5. Sequential Logic Design: R – S Latch, D Latch, Flip flops, SR, JK, T, D, Master /Slave Flip
Pr




Flop, Flip flop excitation tables, Analysis of clocked sequential circuits, Moore /Mealy
y,




models, Registers, Shift Registers, Universal Shift Register. Counters, Asynchronous Ripple
h
at
ap
m
U
V.

, 2


Counters, Synchronous Counters- Ring Counter, Johnson Counter,
Practical: Design of a digital circuit for solving practical problems.
6. System Design: Memory Systems, RAM, ROM, Memory Decoding, error detection and
correction, Digital System Design using PROM, PLA , PAL, FPGA
Activities: Combination of in class & Flipped
Practical:
1. Project demonstration and presentation
2. Mini project on the design of a digital circuit for solving practical problems.
S.No. Description
Unit-I
Boolean Algebra
Prepared by,
V.Umapathy,Prof./Mech.
Basic Concepts




Negative Negative binary numbers are commonly represented using 1’s complement or 2’s
Numbers complement.
1’s Complement Change every 0 → 1 and 1 → 0. Example: 1010 → 0101.
2’s Take 1’s complement and add 1. Example: 1010 → 0101 + 1 = 0110. Mainly used
Complement for signed binary arithmetic.
Binary Addition rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10. Subtraction can be performed using
Arithmetic 2’s complement.
Binary BCD: each decimal digit represented by 4 bits. Gray Code: consecutive values differ by
Codes one bit. ASCII: represents characters using binary codes.
Boolean Algebra dealing with binary variables 0 and 1 and logical operations. Basic
Algebra operations: AND (·), OR (+), NOT (′).
h.

Basic Postulates A+0=AA+0=A, A⋅1=A=A, A+1=1A+1=1, A⋅0=0, A+A=A, A⋅A=A.
ec



Important Complement: A+A′=1, A⋅A′=0A+A'=1,\; A. A'=0. Involution: (A′)′=A(A')'=A.
./M




Theorems Absorption: A+AB=A, A(A+B)=AA+AB=A,\; A(A+B)=A.
of
Pr




De Morgan’s (A+B)′=A′B′(A+B)'=A'B'; (AB)′=A′+B′(AB)'=A'+B'. Very important for
Theorems simplifying logic circuits.
y,
h
at
ap
m
U
V.

, 3


Boolean An expression consisting of Boolean variables and operators. Example: F = AB +
Function A'C.
Truth A table showing all possible input combinations and the corresponding output. For n
Table inputs, number of combinations = 2n2^n.
Logic AND: output 1 only when all inputs are 1. OR: output 1 when any input is 1. NOT:
Gates reverses the input.
Universal NAND and NOR are called universal gates because any basic logic gate or Boolean
Gates function can be implemented using only NAND or only NOR gates.
XOR & XNOR XOR: output 1 when inputs are different. XNOR: output 1 when inputs are the same.
Key Exam Remember: AND = multiplication, OR = addition, NOT = complement, NAND =
Point NOT-AND, NOR = NOT-OR.
Multiple Choice QA
Prepared by,
V.Umapathy,Prof./Mech.
1. Which complement is obtained by changing every 0 to 1 and every 1 to 0 in a binary number?

A) 2’s complement
B) 1’s complement
C) 9’s complement
D) 10’s complement

Answer: B) 1’s complement

Reason: 1’s complement is obtained by simply inverting each binary bit. For example, the 1’s
complement of 10110 is 01001.

2. What is the 2’s complement of the binary number 10101?

A) 01010
B) 01011
C) 10110
D) 01101

Answer: B) 01011
.h
ec


Reason: First find the 1’s complement:
./M




10101 → 01010
Then add 1:
of
Pr




01010 + 1 = 01011
hy,
at
ap
m
U
V.

, 4



Therefore, the 2’s complement is 01011.

3. Which of the following is a universal logic gate?

A) AND
B) OR
C) NAND
D) XOR

Answer: C) NAND

Reason: NAND is called a universal gate because any basic logic gate (AND, OR, NOT) and hence
any Boolean function can be implemented using only NAND gates. NOR is also a universal gate.

4. According to Boolean algebra, what is the result of A+A′A + A'?

A) 0
B) 1
C) A
D) A'

Answer: B) 1

Reason: By the Complement Law of Boolean algebra:

A+A′=1A + A' = 1

A variable ORed with its complement always produces logic 1.

5. What is the hexadecimal equivalent of the binary number 1110 1010?

A) EA
B) AE
C) DA
D) ED
.h
ec



Answer: A) EA
./M
of




Reason: Divide the binary number into groups of four:
Pr
y,
h
at
ap
m
U
V.