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# Combinational circuits

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### Combinational circuits

1. 1. Combinational logic circuits Dr. C. Saritha Lecturer in Electronics SSBN Degree and PG College AnantapurDecember 22, 2012 1
2. 2. overview What is combinational logic circuit ? Examples of combinational logic circuits Binary-adder Binary-subtractor Binary-multiplier Decoders MultiplexersDecember 22, 2012 2
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 .December 22, 2012 3
4. 4. 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
5. 5. Circuit & truthtable of Half-AdderCircuit diagram TruthtableDecember 22, 2012 5
6. 6. 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
7. 7. Circuit diagrams of full-adderDecember 22, 2012 7
8. 8. 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
9. 9. For adding 4-bit binary numbers we need four full-adders as shown below : consider two binary numbers A=1011 & B =0011December 22, 2012 9
10. 10. 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
11. 11. Circuit & truthtable of half- subtractor circuit diagram  TruthtableDecember 22, 2012 11
12. 12. 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
13. 13. Circuit & truthtable of full subtractor circuit diagram  TruthtableDecember 22, 2012 13
14. 14. 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
15. 15. Four-bit adder-subtractorDecember 22, 2012 15
16. 16. 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
17. 17. 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
18. 18. 2-bit by 2-bit multiplier circuitDecember 22, 2012 18
19. 19. 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
20. 20. Three - to - eight line decoder This three - to - eight line decoder is used to binary to octal conversions .December 22, 2012 20
21. 21. 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
22. 22. Four - to - one line multiplexercircuit & truth table :December 22, 2012 22
23. 23. THANK YOUDecember 22, 2012 23
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