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Combinational logic circuitsCombinational logic circuits

Dr. C. SarithaDr. C. SarithaLecturer in ElectronicsLecturer in Electronics

SSBN Degree and PG CollegeSSBN Degree and PG CollegeAnantapurAnantapur

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overviewoverview What is combinational logic circuit ?What is combinational logic circuit ? Examples of combinational logic Examples of combinational logic

circuits circuits Binary-adderBinary-adder Binary-subtractorBinary-subtractor Binary-multiplierBinary-multiplier DecodersDecoders MultiplexersMultiplexers

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Combinational logic circuitCombinational logic circuit Combinational circuits consists of Combinational circuits consists of

logic gates whose outputs depends on logic gates whose outputs depends on the present inputs .They have no the present inputs .They have no memory element .memory element .

It consists of input variables , logic It consists of input variables , logic gates & output variables .gates & output variables .

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Binary-AdderBinary-Adder Half-Adder :Half-Adder : A combinational circuit that performs A combinational circuit that performs

the addition of two bits at a time is called the addition of two bits at a time is called “ Full-Adder ‘’ .“ Full-Adder ‘’ .

The input variables designate the The input variables designate the augend and addend bits ; the output augend and addend bits ; the output variables produce the sum & carry .variables produce the sum & carry .

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Circuit & truthtable of Half-AdderCircuit & truthtable of Half-Adder

Circuit diagramCircuit diagram TruthtableTruthtable

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Full-Adder :Full-Adder : A combinational circuit that performs the A combinational circuit that performs the

addition of three bits at a time is called “ addition of three bits at a time is called “ Full-Adder ’’ Full-Adder ’’

Block diagram & the truth table of Full-Block diagram & the truth table of Full-Adder .Adder .

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Circuit diagrams of full-adderCircuit diagrams of full-adder

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Binary-AdderBinary-Adder A Binary-Adder is a digital circuit that A Binary-Adder is a digital circuit that

produces the arthimatic sum of two produces the arthimatic sum of two binary numbers at a time .binary numbers at a time .

It can also construct by cascading no It can also construct by cascading no of full-adders we get a N-bit binary-of full-adders we get a N-bit binary-adder circuit .adder circuit .

An N-bit adder requires n full-adders An N-bit adder requires n full-adders with each output carry connected to the with each output carry connected to the input carry to the next full-adder .input carry to the next full-adder .

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

consider two binary numbers consider two binary numbers A=1011 & B =0011A=1011 & B =0011

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Binary-subtractorBinary-subtractor Half-subtractor : Half-subtractor : A combinational circuit which performs A combinational circuit which performs

the subtraction of two bits at a time is the subtraction of two bits at a time is called “ Half-subtractor “ .called “ Half-subtractor “ .

It has two inputs & two outputs . The two It has two inputs & two outputs . The two inputs x & y form the minuend & inputs x & y form the minuend & subtrahend & D is the difference output & subtrahend & D is the difference output & B is the borrow output .B is the borrow output .

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Circuit & truthtable of half-Circuit & truthtable of half-subtractorsubtractor

circuit diagramcircuit diagram

TruthtableTruthtable

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Full subtractorFull subtractor

A combinational circuit which A combinational circuit which performs the subtraction of three bits performs the subtraction of three bits at a time is called “ Full subtractor “ .at a time is called “ Full subtractor “ .

A full subtractor has three inputs x y A full subtractor has three inputs x y Bin & two outputs D & Bout .Bin & two outputs D & Bout .

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Circuit & truthtable of full subtractorCircuit & truthtable of full subtractor

circuit diagramcircuit diagram Truthtable Truthtable

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Binary-subtractorBinary-subtractor

The subtraction can be done by taking The subtraction can be done by taking the 2’s compliment of B and adding it the 2’s compliment of B and adding it to A .to A .

2’s compliment can be obtained by 2’s compliment can be obtained by taking the 1’s compliment and adding 1 taking the 1’s compliment and adding 1 to least significant bit .to least significant bit .

1’s compliment can be obtained by 1’s compliment can be obtained by changing 1’s into 0’s & 0’s into 1’s .changing 1’s into 0’s & 0’s into 1’s .

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Four-bit adder-subtractorFour-bit adder-subtractor

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Continues…..Continues…..

In this circuit the mode input m In this circuit the mode input m controls the operation . When m=0 , the controls the operation . When m=0 , the circuit is an adder circuit . When m=1, circuit is an adder circuit . When m=1, the the circuit becomes a subtractor .circuit becomes a subtractor .

The c & v are two outputs . C is for The c & v are two outputs . C is for carry & v is for overflow . If v=0 after an carry & v is for overflow . If v=0 after an addition or subtraction ,then no addition or subtraction ,then no overflow occurred and the n-bit result overflow occurred and the n-bit result is correct . If v=1 , then the result of the is correct . If v=1 , then the result of the operation contains n+1 bits . operation contains n+1 bits .

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Binary-multiplierBinary-multiplier

The multiplication of binary numbers The multiplication of binary numbers is performed in the same way as is performed in the same way as multiplication of decimal numbers .multiplication of decimal numbers .

If we take the multiplication of 2-bit If we take the multiplication of 2-bit numbers . The multiplicand bits are numbers . The multiplicand bits are B1 & B0 , the multiplier bits are A1 & B1 & B0 , the multiplier bits are A1 & A0 and the product is C3,C2,C1,C0 .A0 and the product is C3,C2,C1,C0 .

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2-bit by 2-bit multiplier circuit2-bit by 2-bit multiplier circuit

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DecodersDecoders

A decoder is a combinational circuit A decoder is a combinational circuit that converts binary information from n that converts binary information from n input lines to a maximum of 2n unique input lines to a maximum of 2n unique output lines .output lines .

Generally a decoder is called as n to m Generally a decoder is called as n to m line decoder . line decoder .

A decoder is used to convert binary A decoder is used to convert binary form to any other desired form .form to any other desired form .

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Three - to - eight line decoderThree - to - eight line decoder

This three - to - eight line decoder is This three - to - eight line decoder is used to binary to octal conversionsused to binary to octal conversions . .

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MultiplexerMultiplexer multiplexer is a combinational circuitmultiplexer is a combinational circuit

that selects binary information from that selects binary information from one of many input lines and directs it to one of many input lines and directs it to a single output line .a single output line .

Normally there are 2n input lines and n Normally there are 2n input lines and n selection lines whose bit combinations selection lines whose bit combinations determines which input is selected .determines which input is selected .

A multiplexer is also called ‘ Data A multiplexer is also called ‘ Data selector ’ selector ’

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

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