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Combinational circuits

This document discusses combinational logic circuits such as adders, subtractors, multipliers, decoders, and multiplexers. It provides circuit diagrams and truth tables for half adders, full adders, half subtractors, full subtractors, decoders, and multiplexers. It also describes how to build binary adders and subtractors using these basic components and how multiplication of binary numbers is performed.

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Combinational logic circuits Dr. C. Saritha Lecturer in Electronics SSBN Degree and PG College Anantapur December 22, 2012 1
overview  What is combinational logic circuit ?  Examples of combinational logic circuits  Binary-adder  Binary-subtractor  Binary-multiplier  Decoders  Multiplexers December 22, 2012 2
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 . December 22, 2012 3
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 . December 22, 2012 4
Circuit & truthtable of Half-Adder Circuit diagram Truthtable December 22, 2012 5
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 . December 22, 2012 6
Circuit diagrams of full-adder December 22, 2012 7
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 . December 22, 2012 8
For adding 4-bit binary numbers we need four full-adders as shown below : consider two binary numbers A=1011 & B =0011 December 22, 2012 9
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 . December 22, 2012 10
Circuit & truthtable of half- subtractor  circuit diagram  Truthtable December 22, 2012 11
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 . December 22, 2012 12
Circuit & truthtable of full subtractor  circuit diagram  Truthtable December 22, 2012 13
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 . December 22, 2012 14
Four-bit adder-subtractor December 22, 2012 15
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 . December 22, 2012 16
Binary-multiplier  The multiplication of binary numbers is performed in the same way as multiplication of decimal numbers .  If we take the multiplication of 2-bit numbers . The multiplicand bits are B1 & B0 , the multiplier bits are A1 & A0 and the product is C3,C2,C1,C0 . December 22, 2012 17
2-bit by 2-bit multiplier circuit December 22, 2012 18
Decoders  A decoder is a combinational circuit that converts binary information from n input lines to a maximum of 2n unique output lines .  Generally a decoder is called as n to m line decoder .  A decoder is used to convert binary form to any other desired form . December 22, 2012 19
Three - to - eight line decoder  This three - to - eight line decoder is used to binary to octal conversions . December 22, 2012 20
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 ’ December 22, 2012 21
Four - to - one line multiplexer circuit & truth table : December 22, 2012 22
THANK YOU December 22, 2012 23