Digital Circuits & Logic Design Notes
Subject Overview
Digital Circuits & Logic Design covers number systems and logic gates, Boolean algebra and combinational circuits (adders/
Subject at a glance
4
Units
22
Topics
4
Credits
4
Infographics
Unit-wise Syllabus
4 units — open any unit for detailed topic-wise notes, diagrams and important exam questions
- Decimal/binary/octal/hexadecimal number systems
- conversions
- 1's and 2's complement
- AND/OR/NOT/NAND/NOR/XOR/XNOR gates
- NAND and NOR as universal gates
- logic gate applications
AND
1
0
OR
1
1
NAND
0
1
NOR
0
0
XOR
0
1
Study guide
This unit starts with number systems and their conversions, 1's and 2's complement, and the logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR), with NAND and NOR as universal gates. Practise complement-based subtraction; it is a frequent numerical.
- Boolean algebra theorems
- SOP and POS forms
- K-map simplification
- half/full adders and subtractors
- parallel binary adder
- binary adder/subtractor
De Morgan's theorems
(A + B)' = A'B' and (AB)' = A' + B'
Absorption
A + AB = A
Half adder
Sum = A ⊕ B, Carry = AB
Full adder
Sum = A ⊕ B ⊕ Cin, Cout = AB + Cin(A ⊕ B)
Study guide
You study Boolean algebra theorems, SOP and POS forms, K-map simplification and combinational circuits: half and full adders and subtractors, parallel binary adders and adder-subtractors. Always draw the truth table first and simplify with a K-map.
- Multiplexers and demultiplexers
- encoders and decoders
- latches
- R-S/J-K/Master-Slave J-K/D/T flip-flops
- race condition and its removal
- flip-flop applications
SR
Set, Reset
S = R = 1 is invalid
JK
J, K
J = K = 1 toggles
D
Data
Output follows D on the clock
T
Toggle
T = 1 toggles the output
Study guide
You study multiplexers, demultiplexers, encoders, decoders and sequential circuits: latches and R-S, J-K, master-slave J-K, D and T flip-flops, the race condition and its removal and applications. Memorise each flip-flop's truth table.
- Clock pulse generation using a 555 timer as monostable and multivibrator
- design of asynchronous and synchronous counters
- up-down counters
- MOD-N counters
Clock
Only the first flip-flop
All flip-flops together
Speed
Slower: delays add up
Faster
Design
Simple
More complex
Glitches
More likely
Fewer
Study guide
You study clock generation with a 555 timer in monostable and astable modes, and the design of asynchronous and synchronous counters, up-down counters and MOD-N counters. Practise designing a MOD-N counter from state tables.
Why Digital Circuits & Logic Design Matters
Digital logic explains how processors and memory are built, and it is the basis for computer architecture, embedded systems and electronics careers.
How to Prepare for Digital Circuits & Logic Design
- Practise K-map simplification and adder design.
- Learn flip-flop truth tables and excitation tables.
- Draw neat circuit diagrams in your answers.
Digital Circuits & Logic Design: Frequently Asked Questions
What is a universal gate?
A universal gate, NAND or NOR, can be used alone to build any other logic gate and therefore any digital circuit.
What is the difference between synchronous and asynchronous counters?
In a synchronous counter all flip-flops share the same clock, while in an asynchronous counter each flip-flop is triggered by the output of the previous one.