Download to read offline
ABOUT THE DIGITAL ELECTRONIC TOPIC CIRCUIT DESIGN
- 1. overview overview What iscombinational logic circuit ? What is combinational logic circuit ? Examples of combinational logic Examples of combinational logic circuits circuits Binary-adder Binary-adder Binary-subtractor Binary-subtractor Binary-multiplier Binary-multiplier Decoders Decoders Multiplexers Multiplexers November 30, 2024 November 30, 2024 1 1
- 2. Combinational logic circuit Combinationallogic 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 . November 30, 2024 November 30, 2024 2 2
- 3. Binary-Adder Binary-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 . November 30, 2024 November 30, 2024 3 3
- 4. Circuit & truthtableof Half-Adder Circuit & truthtable of Half-Adder Circuit diagram Circuit diagram Truthtable Truthtable November 30, 2024 November 30, 2024 4 4
- 5. November 30, 2024 November30, 2024 5 5 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 .
- 6. Circuit diagrams offull-adder Circuit diagrams of full-adder November 30, 2024 November 30, 2024 6 6
- 7. Binary-Adder Binary-Adder A Binary-Adderis 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 . November 30, 2024 November 30, 2024 7 7
- 8. For adding 4-bitbinary numbers we For adding 4-bit binary numbers we need four full-adders as shown below : need four full-adders as shown below : November 30, 2024 November 30, 2024 8 8 consider two binary numbers consider two binary numbers A=1011 & B =0011 A=1011 & B =0011
- 9. Binary-subtractor Binary-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 . November 30, 2024 November 30, 2024 9 9
- 10. Circuit & truthtableof half- Circuit & truthtable of half- subtractor subtractor circuit diagram circuit diagram Truthtable Truthtable November 30, 2024 November 30, 2024 10 10
- 11. Full subtractor Full 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 . November 30, 2024 November 30, 2024 11 11
- 12. Circuit & truthtableof full subtractor Circuit & truthtable of full subtractor circuit diagram circuit diagram Truthtable Truthtable November 30, 2024 November 30, 2024 12 12
- 13. Binary-subtractor Binary-subtractor The subtractioncan 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 . November 30, 2024 November 30, 2024 13 13
- 14. Four-bit adder-subtractor Four-bit adder-subtractor November30, 2024 November 30, 2024 14 14
- 15. Continues….. Continues….. In thiscircuit 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 . November 30, 2024 November 30, 2024 15 15
- 16. Binary-multiplier Binary-multiplier November 30, 2024 November30, 2024 16 16 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 .
- 17. 2-bit by 2-bitmultiplier circuit 2-bit by 2-bit multiplier circuit November 30, 2024 November 30, 2024 17 17
- 18. Decoders Decoders A decoderis 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 . November 30, 2024 November 30, 2024 18 18
- 19. Three - to- eight line decoder Three - to - eight line decoder This three - to - eight line decoder is This three - to - eight line decoder is used to binary to octal conversions used to binary to octal conversions . . November 30, 2024 November 30, 2024 19 19
- 20. Multiplexer Multiplexer multiplexer isa combinational circuit multiplexer 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 ’ November 30, 2024 November 30, 2024 20 20
- 21. Four - to- one line multiplexer Four - to - one line multiplexer circuit & truth table : circuit & truth table : November 30, 2024 November 30, 2024 21 21
- 22. THANK YOU THANK YOU November30, 2024 November 30, 2024 22 22