The document is a presentation on combinational logic circuits. It discusses different types of combinational logic circuits including adders, half adders, full adders, subtractors, half subtractors, full subtractors, and universal gates. It also discusses implementing logic gates using NAND and NOR gates and how to implement an XOR gate using NAND gates.

1. Combinational Logic
Presentation on
Chapter-4

2. 28-Jul-19 2
Prepared For
SN Name ID No Program
01 Rihab Rahman CONFIDENTIAL BCSE
02 Rakib Uddin CONFIDENTIAL BCSE
03 Saifullah Al Mamun CONFIDENTIAL BCSE
04 Tufail Ahmed CONFIDENTIAL BCSE
05 Shuvo Saha CONFIDENTIAL BCSE
Prepared By

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Contents
❖Combinational Logic Circuit
❖Adder
❖Half Adder
❖Full Adder
❖Half Subtractor
❖Full Subtractor
❖Universal Gate
❖Universal Gate (NAND)
❖Universal Gate (NOR)
❖NAND Gate - Invert OR
❖NOR Gate – Invert AND
❖XOR Implementation
Rihab Rahman

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Combinational Logic Circuit
The combinational logic circuits in digital circuit theory can
be defined as a type of digital logic circuit implemented using
Boolean circuits, where the output of logic circuit is a pure
function of the present inputs only.
Rihab Rahman

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Adder
A combinational logic circuit that perform addition between
two or more bits and produces sum and carry is called adder.
There are two types of adder. They are -
❖Half Adder
❖Full Adder
Rihab Rahman

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Half Adder
A combinational logic circuit that perform addition between
two bits and produces carry and sum is called half adder.
S = A⊕B = A’B + AB’
C = A.B
Rihab Rahman

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Full Adder
A combinational logic circuit that perform addition between
three bits and produces carry and sum is called full adder.
Fig: Block Diagram of Full Adder
Rihab Rahman

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Full Adder
S = ((A ⊕ B) ⊕ C)
Cout = (A ⊕ B) C + AB
Rihab Rahman

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Subtractor
A combinational logic circuit that perform subtraction
between two or more bits and produces difference and
borrow is called subtractor. There are two types of
subtractor. They are -
❖Half Subtractor
❖Full Subtractor
Tufail Ahmed

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Half Subtractor
A CL circuit that perform subtraction between two bits and
produces difference and borrow is called half subtractor.
D = A ⊕ B
Bo = A’B Tufail Ahmed

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Full Subtractor
A CL circuit that perform subtraction between two bits,
taking into account that a 1 may have been borrowed by a
lower significant stage and produces difference and borrow
is called half subtractor.
Fig: Block Diagram of Full Subtractor
Tufail Ahmed

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Full Subtractor
D=A ⊕ B ⊕ BORin
BORout= BORin.((A ⊕ B))’ +A’.B
Rakib Uddin

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Universal Gate
A universal gate is a gate which can implement any Boolean
function without need to use any other gate type. The NAND
and NOR gates are universal gates. They can perform as like
as the basic gates.
Rakib Uddin

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Universal Gate (NAND)
Rakib Uddin

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Universal Gate (NOR)
Rakib Uddin

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NAND Gate - Invert OR
Applying DeMorgan's Law: Invert-OR = NAND
This NAND symbol is called Invert-OR. Since inputs are
inverted and then ORed together. AND-Invert & Invert-OR
both represent NAND gate
Saifullah Al Mamun

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NOR Gate – Invert AND
The Invert-AND symbol is also used for NOR
This NOR symbol is called Invert-AND, since inputs are
inverted and then ANDed together. OR-Invert & Invert-
AND both represent NOR gate.
Saifullah Al Mamun

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XOR Implementation
The XOR gate is a digital logic gate that gives a true (1 or
HIGH) output when the number of true inputs is odd. If both
inputs are false (0/LOW) or both are true, a false output
results.
Fig: XOR Implementation by NAND
Saifullah Al Mamun

19. 28-Jul-19 19Saifullah Al Mamun