This document provides an overview of combinational logic circuits such as adders, subtractors, and multiplexers. It describes half adders and full adders that perform binary addition of two and three bits respectively. Binary adders can be constructed by cascading full adders. Binary subtractors use half and full subtractors to perform subtraction by taking the 2's complement of one number and adding it to the other. An example circuit is shown that can function as either an adder or subtractor based on a mode input. Finally, multiplexers are described as circuits that select one of several input lines to output based on selection lines.

1. 1
Combinational logic circuits
Amjad Hassan Khan MK
Lecturer in Electronics
Kristu Jayanti College,
Bangalore

2. 2
overview
 What is combinational logic circuit ?
 Examples of combinational logic
circuits
 Binary-adder
 Binary-subtractor
Multiplexers

3. 3
Combinational logic circuit
 Combinational circuits consists of
logic gates whose outputs depends on
the present inputs .They have no
memory element .
 It consists of input variables , logic
gates & output variables .

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Binary-Adder
 Half-Adder :
 A combinational circuit that performs
the addition of two bits at a time is called
“ Full-Adder ‘’ .
 The input variables designate the
augend and addend bits ; the output
variables produce the sum & carry .

5. 5
Circuit & truthtable of Half-Adder
Circuit diagram Truthtable

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Full-Adder :
 A combinational circuit that performs the
addition of three bits at a time is called “
Full-Adder ’’
 Block diagram & the truth table of Full-
Adder .

7. 7
Circuit diagrams of full-adder

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Binary-Adder
 A Binary-Adder is a digital circuit that
produces the arthimatic sum of two
binary numbers at a time .
 It can also construct by cascading no
of full-adders we get a N-bit binary-
adder circuit .
 An N-bit adder requires n full-adders
with each output carry connected to the
input carry to the next full-adder .

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For adding 4-bit binary numbers we
need four full-adders as shown
below :

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Binary-subtractor
 Half-subtractor :
 A combinational circuit which
performs the subtraction of two bits at
a time is called “ Half-subtractor “ .
 It has two inputs & two outputs . The
two inputs x & y form the minuend &
subtrahend & D is the difference
output & B is the borrow output .

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Circuit & truthtable of half-
subtractor
 circuit diagram  Truthtable

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Full subtractor
 A combinational circuit which
performs the subtraction of three bits
at a time is called “ Full subtractor “ .
 A full subtractor has three inputs x y
Bin & two outputs D & Bout .

13. 13
Circuit & truthtable of full subtractor
 circuit diagram  Truthtable

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Binary-subtractor
 The subtraction can be done by taking
the 2’s compliment of B and adding it
to A .
 2’s compliment can be obtained by
taking the 1’s compliment and adding 1
to least significant bit .
 1’s compliment can be obtained by
changing 1’s into 0’s & 0’s into 1’s .

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Four-bit adder-subtractor

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Continues…..
 In this circuit the mode input m
controls the operation . When m=0 , the
circuit is an adder circuit . When m=1,
the circuit becomes a subtractor .
 The c & v are two outputs . C is for
carry & v is for overflow . If v=0 after an
addition or subtraction ,then no
overflow occurred and the n-bit result
is correct . If v=1 , then the result of the
operation contains n+1 bits .

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Multiplexer
 multiplexer is a combinational circuit
that selects binary information from
one of many input lines and directs it to
a single output line .
 Normally there are 2n input lines and n
selection lines whose bit combinations
determines which input is selected .
 A multiplexer is also called ‘ Data
selector ’

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Four - to - one line multiplexer
circuit & truth table :

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