Digital Logic - AND, OR, NOT, NAND, NOR Gates

1. DIGITAL LOGIC
 What is gate?
 The Basic Gates
 NOT gate
 OR gate
 AND gate
 Universal Logic Gates
 NOR gate
 NAND gate
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Presented by,
M.Madhu Bala

2. GATES
 A digital circuit having one or more input signals but only one
output signal is called a gate.
 Connecting the basic gates in different ways makes it
possible to produce circuits.
 Gates are often called logic circuits.
 The basic gates can be used to produce any digital system.
 The three basic logic circuits are
 the inverter (NOT)
 the OR gate and
 the AND gate
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3. THE INVERTER (NOT GATE)
 A NOT gate has one input signal and one output signal.
 The output Y of NOT gate is always complement of input A.
 In equation form
Y= NOT A Y=A‘ Y=A
 There are only two possible voltage levels (low and high) associated
with a digital circuit. This fits with the binary number system (0&1)
 This is often referred to as two-state operation.
 In the positive logic,
 the higher voltage level is assigned the binary value 1 (H=1)
 the lower voltage level is assigned the binary value 0 .(L=0)
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A Y=A’
L H
H L
A Y=A’
0 1
1 0
Logic Circuit of NOT gate
Truth Table

4. THE INVERTER (NOT GATE)
TTL NOT Gates
Pinout diagram of a 7404 hex inverter
 This IC contains six inverters.
 After applying +5 V to pin 14 and grounding pin 7, you can connect
any or all inverters to other Transistor–Transistor Logic(TTL) devices.
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5. OR GATE
 An OR gate has two or more input signals but only one output
signal.
 It is called an OR gate because the output voltage is high if any or
all of the input voltages are high.
 In Boolean equation form
Y = A OR B Y = A + B
The '+' sign represents the logic operation OR
 The number of rows in a truth table equals 2n, where n is the
number of inputs
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Logic Circuit of OR gate
A B Y=A+B
0 0 0
0 1 1
1 0 1
1 1 1
Truth Table

6. Three- input OR gate
 The inputs are A, B, and C.
 When all inputs are low, the output is low.
 If any input is high, the output will be high.
 Boolean Equation Form:
Y = A+B+C
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OR GATE (CONT..)
A B C Y=A+B+C
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1Logic Circuit of 3-input OR gate
Truth Table

7. TTL OR Gates
This digital IC contains four 2-input OR gates inside a 14-
pin DIP.
After connecting a supply voltage of +5 V to pin 14 and a
ground to pin 7, you can connect one or more of the OR
gates to other TTL devices.
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OR GATE (CONT.)

8. Timing diagram for 2-input OR gate
 The input voltages drive pins 1 and 2 of a 7432.
 The output (pin 3) is low only when both inputs are low.
 The output is high the rest of the time.
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OR GATE (CONT..)

9.  The AND gate has a high output only when all inputs are high.
otherwise the output will be low.
 AND gate also known as all-or-nothing gate.
 In Boolean equation form
Y =A AND B Y=A.B Y=AB
The '.' sign represents the logic AND operation.
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AND GATE
A B Y=AB
0 0 0
0 1 0
1 0 0
1 1 1Logic Circuit of AND gate
Truth Table

10. Three- input AND gate
 The inputs are A, B, and C.
 When all inputs are high, the output is high.
 If even one input is low, the output is in the low state.
 In Boolean equation form:
Y=A.B.C Y=ABC
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AND GATE (CONT..)
A B C Y=ABC
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
Logic Circuit of AND gate
Truth Table

11. TTL AND Gates
 This digital IC contains four 2-input AND gates.
 After connecting a supply voltage of +5V to pin 14 and a ground to
pin 7, you can connect one or more of the AND gates to other TTL
devices.
 TTL AND gates are also available in triple 3-input and dual 4-input
packages.
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AND GATE (CONT..)

12. Timing diagram for a 2-input AND gate
The input voltages drive pins 1 and 2 of a 7408.
the output (pin 3) is high only when both inputs are high.
The output is low the rest of the time.
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AND GATE (CONT..)

13. The NAND & NOR gates are called universal gates because
they can perform all the logical operations of basis gates like
AND, OR, NOT.
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Universal Logic Gate

14.  The circuit of NOR gate is a circuit of OR gate followed by an inverter
 The output of NOR gate is
Y=A+B
 NOR Gates also called a NOT-OR gate.
 All inputs must be low to get a high output.
 If any input is high, the output is low.
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NOR GATE
Logic Circuit of NOR Gates
Abbreviated form Standard form IEEE form
Truth Table
A B Y=(A+B)’
0 0 1
0 1 0
1 0 0
1 1 0

15. Pin- out Diagram of NOR gate
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NOR GATE (CONT.)

16. Bubbled AND Gate
 Bubbled AND Gate inverters on the input lines of an AND gate.
 The output of bubbled AND gate and NOR gate are identical.
 Therefore, these two circuits are equivalent and thus
interchangeable.
 The output of bubbled AND gate is represented as
Y= A . B
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NOR GATE (CONT.)
Abbreviated form Standard form
Truth Table
A B A’ B’ Y=A’.B’
0 0 1 1 1
0 1 1 0 0
1 0 0 1 0
1 1 0 0 0
Logic Circuit of Bubbled AND Gates

17. De Morgan's First Theorem
NOR gate : Y=(A+B)’
bubbled AND gate : Y=A’B’
 The outputs are equal for the same inputs, so that (A+B)’ = A’B’
 The complement of a sum equals the product of the complements.
This identity is known as De Morgan’s, first theorem.
 This can also be proved by comparing the truth tables of NOR and
bubbled AND gates.
 Three input NOR gate and three input bubbled AND gate are
identical and it can write, (A+ B + C)' = A'B'C'
 This equivalence can be extended to gates or circuits for larger
number of inputs, too.
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NOR GATE (CONT.)

18. NOT from NOR
 To get a NOT gate, tie inputs of NOR gate together so that there is
only one input to the circuit.
 If input is 0, then both the inputs to NOR gate are 0 that gives output
1.
 Similarly, if input is 1, both the inputs to NOR gate are 1 that gives
output 0.
 Therefore the output of circuit is complement of its input and thus
gives NOT operation.
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NOR GATE (CONT.)

19. OR from NOR
 To get a OR gate, two NOR gates are used.
 The first NOR gate performs usual NOR operation.
 The second NOR gate performs as NOT gate and inverts the
NOR logic to OR
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NOR GATE (CONT.)
A+B

20. AND from NOR
 To get a AND gate, three NOR gates are used.
 The first and second NOR gate performs as NOT gate.
 NOT gates are replaced by NOR equivalent. Since NOR gate is
NOT operation followed by OR we invert the
 output of example 2.3, shown in Fig. 2.9b to get output of this
circuit. Thus output of circuit in Fig. 2.2 lc is
 high only when both the inputs are high and it functions like an
AND gate.
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NOR GATE (CONT.)

21.  The circuit of NAND gate is a circuit of AND gate followed by an
inverter
 The output of NAND gate is
Y=AB "Y equals NOT A AND B"
 NAND Gates also called a NOT-AND gate.
 All inputs must be high to get a low output.
 If any input is low, the output is high.
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NAND GATE
Logic Circuit of NAND Gate
Abbreviated form Standard form IEEE form
Truth Table
A B AB Y=AB
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0

22. Pin- out Diagram of NAND gate
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NAND GATE (CONT.)

23. Bubbled OR Gate
 Bubbled OR Gate inverters on the input lines of an OR gate.
 The output of bubbled OR gate and NAND gate are identical.
 Therefore, these two circuits are equivalent and thus
interchangeable.
 The output of bubbled OR gate is represented as
Y=A+B
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NAND GATE (CONT.)
A B A B Y=A+B
0 0 1 1 1
0 1 1 0 1
1 0 0 1 1
1 1 0 0 0
Abbreviated form Standard form
Truth TableLogic Circuit of Bubbled OR Gate

24. De Morgan's Second Theorem
NAND Gate :(AB)’
Bubbled OR Gate : Y=A’+B’
 The outputs are equal for the same inputs, so that (AB)’ = A’+B’
 The complement of a product equals the sum of the complements.
This identity is known as De Morgan’s second theorem.
 This can also be proved by comparing the truth tables of NAND gate
and bubbled OR gate.
 Three input NAND gate and three input bubbled OR gate are identical
and it can write, (ABC)' = A’+B‘+C’
 This equivalence can be extended to gates or circuits with any number
of inputs.
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NAND GATE (CONT.)

25. THANK YOU
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