4:Combinational logic circuits. 3 July

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Godfrey Holland
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1 4:Combinational logic circuits 3 July

2 overview What is combinational logic circuit? Examples of combinational logic circuits Binary-adder Binary-subtractor Binary-multiplier Decoders Multiplexers 3 July

3 Learning Objectives Explore the application of Boolean algebra in the design of electronic circuits. The basic elements of circuits are gates. Each type of gate implements a Boolean operation. We will study combinational circuits - the circuits whose output depends only on the input and not on the current state of the circuit (no memory). 3

4 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. 3 July

5 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. 3 July

6 Circuit & truthtable of Half-Adder Circuit diagram Truthtable 3 July

7 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. 3 July

8 Circuit diagrams of full-adder 3 July

9 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 fulladders 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. 3 July

10 For adding 4-bit binary numbers we need four full-adders as shown below : consider two binary numbers A=1011 & B = July

11 Binary-subtractor Half-subtractor : A combinational circuit which performs the subtraction of two bits at a time is called Halfsubtractor. 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. 3 July

12 Circuit & truthtable of halfsubtractor circuit diagram Truthtable 3 July

13 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. 3 July

14 Circuit & truthtable of full subtractor circuit diagram Truthtable 3 July

15 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. 3 July

16 Four-bit adder-subtractor 3 July

17 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. 3 July

18 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. 3 July

19 2-bit by 2-bit multiplier circuit 3 July

20 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. 3 July

21 Three - to - eight line decoder This three - to - eight line decoder is used to binary to octal conversions. 3 July

22 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 3 July

23 Four - to - one line multiplexer circuit & truth table : 3 July

24 THANK YOU 3 July

COMBINATIONAL CIRCUIT

Combinational circuit is a circuit in which we combine the different gates in the circuit, for example encoder, decoder, multiplexer and demultiplexer. Some of the characteristics of combinational circuits