12.Digital Logic

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Logic gate
Logic gates are the basic building blocks of any digital system. It is an electronic circuit
having one or more than one input and only one output.
Types
 AND Gate
 OR Gate
 NOT Gate
 NAND Gate
 NOR Gate
 XOR Gate
AND Gate
A circuit which performs an AND operation is shown in figure. It has n input (n >= 2) and
one output.
 Logic diagram
Truth Table
Digital Logic Circuit

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OR Gate
A circuit which performs an OR operation is shown in figure. It has n input (n >= 2) and one
output.
Logic diagram
Truth Table
NOT Gate
NOT gate is also known as Inverter. It has one input A and one output Y.
 Logic diagram

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Truth Table
NAND Gate
A NOT-AND operation is known as NAND operation. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
NOR Gate
A NOT-OR operation is known as NOR operation. It has n input (n >= 2) and one output.

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Logic diagram
Truth Table
XOR Gate
XOR or Ex-OR gate is a special type of gate. It can be used in the half adder, full adder and
subtractor. The exclusive-OR gate is abbreviated as EX-OR gate or sometime as X-OR gate.
It has n input (n >= 2) and one output.
Logic diagram
Truth Table

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XNOR Gate
XNOR gate is a special type of gate. It can be used in the half adder, full adder and subtractor.
The exclusive-NOR gate is abbreviated as EX-NOR gate or sometime as X-NOR gate. It has
n input (n >= 2) and one output
Logic diagram
Truth Table
NAND and NOR Universal Gate
 NAND and NOR are called universal gates because all the other gates like
and,or,not,xor and xnor can be derived from it.
 Any basic gate can be implemented using NAND and NOR.

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De Morgan's Theorems
 De Morgan has suggested two theorems which are extremely useful in
Boolean Algebra.
Theorem 1
 The left hand side (LHS) of this theorem represents a NAND gate with inputs A and
B, whereas the right hand side (RHS) of the theorem represents an OR gate with
inverted inputs.

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This OR gate is called as Bubbled OR.
Table showing verification of the De Morgan's first theorem –
Theorem 2
The LHS of this theorem represents a NOR gate with inputs A and B, whereas the RHS
represents an AND gate with inverted inputs.

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his AND gate is called as Bubbled AND.
Table showing verification of the De Morgan's second theorem –
Half Adder
Half adder is a combinational logic circuit with two inputs and two outputs. The half adder
circuit is designed to add two single bit binary number A and B. It is the basic building block
for addition of two single bit numbers. This circuit has two outputs carry and sum.

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Truth Table
Circuit Diagram
Full Adder
Full adder is developed to overcome the drawback of Half Adder circuit. It can add two one-
bit numbers A and B, and carry c. The full adder is a three input and two output
combinational circuit.
Truth Table

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Circuit Diagram
Full adder using two half adder
K-map
Karnaugh introduced a method for simplification of Boolean functions in an easy way. This
method is known as Karnaugh map method or K-map method. It is a graphical method, which
consists of 2n cells for ‘n’ variables.
Variable K-Map

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Variable K-Map
Variable K-Map
Example
Let us simplify the following Boolean function, f(W, X, Y, Z)= WX’Y’ + WY + W’YZ’
using K-map.

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Simplified Boolean function is: f= WX’ + WY + YZ’
Example
Let us simplify the following Boolean function, f(X,Y,Z)=∏M(0,1,2,4) using K-map.
Simplified Boolean function is: f=(X+Y).(Y+Z).(Z+X)

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Latch
There are two types of memory elements based on the type of triggering that is suitable to
operate it.
1. Latches
2. Flip-flops
 Latches operate with enable signal, which is level sensitive. Whereas, flip-flops
are edge sensitive. We will discuss about flip-flops in next chapter. Now, let us
discuss about SR Latch & D Latch one by one.
 SR latch example
Flip-flops
 A flip-flop or latch is a circuit that has two stable states and can be used to store state
information. A flip-flop is a bistable multivibrator. The circuit can be made to change
state by signals applied to one or more control inputs and will have one or two
outputs. It is the basic storage element in sequential logic. Flip-flops and latches are
fundamental building blocks of digital electronics systems used in computers,
communications, and many other types of systems
 There are mainly four types of flip flops that are used in electronic circuits. They are
1. The basic Flip Flop or S-R Flip Flop
2. Delay Flip Flop [D Flip Flop]
3. J-K Flip Flop
4. T Flip Flop
S-R Flip Flop
 The SET-RESET flip flop is not designed with the help of two NOR gates and also
two NAND gates. These flip flops are also called S-R Latch.

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S-R Flip Flop using NOR Gate
S-R Flip Flop using NAND Gate

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J-K Flip Flop
Difference between CISC and RISC
CISC RISC
It is prominent on Hardware It is prominent on the software
It has high cycles per second It has low cycles per second
It has transistors used for storing Instructions
which are complex
More transistors are used for storing memory
LOAD and STORE memory to memory is
induced in instructions
LOAD and STORE register to register are
independent
It has multi-clock It has single-clock

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1. The output of an AND gate with three inputs, A, B, and C, is HIGH when ________.
A) A = 1, B = 1, C = 0 B)A = 0, B = 0, C = 0 C)A = 1, B = 1, C = 1 D)A = 1, B = 0, C = 1
2. If a 3-input NOR gate has eight input possibilities, how many of those possibilities will
result in a HIGH output?
A. 1 B. 2 C. 7 D. 8
3. If a signal passing through a gate is inhibited by sending a LOW into one of the inputs,
and the output is HIGH, the gate is a(n):
A. AND B. NAND C. NOR D. OR
4. A device used to display one or more digital signals so that they can be compared to
expected timing diagrams for the signals is a:
A. DMM B. spectrum analyzer C. logic analyzer D. frequency counter
5. When used with an IC, what does the term QUAD indicate?
A. 2 circuits B. 4 circuits C. 6 circuits D. 8 circuits
6. The output of an OR gate with three inputs, A, B, and C, is LOW when ________.
A) A = 0, B = 0, C = 0 B) A = 0, B = 0, C = 1 C) A = 0, B = 1, C = 1 D) all of the above
7. Which of the following logical operations is represented by the + sign in Boolean algebra?
A. inversion B. AND C. OR D. complementation
8. Output will be a LOW for any case when one or more inputs are zero for a(n):
A. OR gate B. NOT gate C. AND gate D. NOR gate
9. How many pins does the 4049 IC have?
A. 14 B. 16 C. 18 D. 20
10. Which of the following choices meets the minimum requirement needed to create
specialized waveforms that are used in digital control and sequencing circuits?
A. basic gates, a clock oscillator, and a repetitive waveform generator
B. basic gates, a clock oscillator, and a Johnson shift counter
C. basic gates, a clock oscillator, and a DeMorgan pulse generator
D. basic gates, a clock oscillator, a repetitive waveform generator, and a Johnson shift counter
1 2 3 4 5 6 7 8 9 10
C A B C B A C C B A
Model Test Answer
Model Test