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# Syllabus........................................................................................................................................ 2
Intorduction............................................................................................................................... 2
Boolean Algebra ........................................................................................................................ 2
Combinational Logical Circuits............................................................................................... 2
Sequential logical circuits......................................................................................................... 2
Counters..................................................................................................................................... 2
Registers..................................................................................................................................... 2
Detection and correction codes ................................................................................................ 2
#1 Introduction............................................................................................................................... 6
Digital Computers..................................................................................................................... 6
Logic Gates ................................................................................................................................ 6
Gate Propagation Delay ........................................................................................................... 8
Universal Gates ......................................................................................................................... 8
NAND gate as a Universal Gate ............................................................................................. 8
#2 Boolean Algebra...................................................................................................................... 10
Boolean Algebra ...................................................................................................................... 10
Boolean Operations................................................................................................................. 10
Basic Identities of Boolean Algebra....................................................................................... 10
DeMorgan’s theorem .............................................................................................................. 11
Complement of a function ...................................................................................................... 12
Simplification using Karnaugh Maps ................................................................................... 12
Variable Maps....................................................................................................................... 12
Sum-of-Products Simplification ............................................................................................ 13
Product-of-Sums Simplification ............................................................................................ 15
NAND and NOR Implementation ........................................................................................ 17
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Don' Care Conditions............................................................................................................ 17
#3 Combinational Logical Circuits ............................................................................................. 18
Combinational Circuits .......................................................................................................... 18
Half-Adder............................................................................................................................... 18
Full-Adder ............................................................................................................................... 18
Parallel Adder ......................................................................................................................... 19
Operation............................................................................................................................... 20
Serial Adder............................................................................................................................. 20
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Construction.......................................................................................................................... 20
Operation............................................................................................................................... 21
Subtractors .............................................................................................................................. 22
Half-subtractor ...................................................................................................................... 22
Full-subtractor....................................................................................................................... 22
Code Converters...................................................................................................................... 23
Decoders................................................................................................................................... 25
NAND Gate Decoder............................................................................................................ 27
Decoder Expansion ............................................................................................................... 27
Encoders................................................................................................................................... 28
Multiplexer .............................................................................................................................. 29
DeMultiplexer.......................................................................................................................... 29
#4 Sequential logic circuits.......................................................................................................... 32
Flip-flops .................................................................................................................................. 32
SR Flip-Flop ............................................................................................................................ 32
SR Flip-Flop circuit with NAND gate .................................................................................. 33
D Flip-Flop............................................................................................................................... 33
D Flip-Flop with NAND gate ............................................................................................... 34
JK Flip-Flop ............................................................................................................................ 34
T Flip-Flop............................................................................................................................... 35
Master-Slave JK Flip-Flop..................................................................................................... 36
Flip-Flop Excitation Tables.................................................................................................... 37
Sequential Circuits.................................................................................................................. 38
Design Procedure .................................................................................................................. 38
#5 Registers .................................................................................................................................. 39
Registers................................................................................................................................... 39
Shift Registers.......................................................................................................................... 40
Bidirectional Shift Register with parallel load..................................................................... 40
Application of Shift Registers ................................................................................................ 41
#6 Counters .................................................................................................................................. 42
Introduction............................................................................................................................. 42
Binary Counters ...................................................................................................................... 42
Synchronous Counters .......................................................................................................... 42
Up counters ....................................................................................................................... 42
Binary Up-Down counters ................................................................................................ 43
Asynchronous counters......................................................................................................... 43
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Up Counters ...................................................................................................................... 43
Down counters .................................................................................................................. 44
Error detection and correction codes.................................................................................... 44
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