Combinational Logic - Digital Logic Design (EEE 241)
Combinational LogicBy : Ali Mustafa
Contents ultiplexer
How to Analyze any combinationalcircuit like this?
Analysis Procedure To obtain the output Boolean functions from alogic diagram:1.Label all gate outputs that are a function of inputvariables.2.Label the gates that are a function of inputvariables and previous labeled gates with differentarbitrary symbols.3.Repeat step 2 until the outputs of the circuit areobtained in terms of the input variables.
Analysis Procedure
Analysis Procedure
Analysis Procedure
Analysis Procedure Derivation of Truth Table
Analysis Procedure
Analysis Procedure
Summary :How to design a combinational circuit?1. Determine the required number ofinputs and outputs.2.Derive the Truth Table.3.Obtain the simplified Boolean functions.4.Draw the logic diagram.
Example Design a combinational circuit with threeinputs and one output. The output must equal “1” when the inputsare less than three and “0” otherwise. [useonly NAND gates]
Example (cont.)1-The system have three inputs and one output
Example (cont.)2-Derive the truth table
Example (cont.)
Circuits to be Implemented Arithmetic circuits–Half Adder–Full Adder–Binary Adder/Subtractor–Binary Multiplier Magnitude Comparator
What's the example of ArithmeticCircuit?One of the famous Digital Logic Circuits isthe calculator.
Arithmetic circuits An arithmetic circuit is a combinational circuit thatperforms arithmetic operations such as addition,subtraction, multiplication and division with binarynumbers or with decimal numbers in a binary code. A combinational circuit that performs the addition oftwo bits is called a “Half Adder”.
Half adder It is required to design a combinational circuitthat adds two binary numbers and producethe output in the form of two bits sum andcarrySolution1- We need to determine the inputs and output ofthe system and give letters for all of them our systemhas two inputs (X, Y) and two outputs (S, C)
Half adder2-Derive the truth table according to the givenrelation between outputs and inputs– In the half adder block the output equals the sumof two binary inputs
Half adder (cont.)3-4-Obtain the simplified Boolean functions foreach output as a function of the input variablesusing K-mapDraw the logic diagram
Full Adder It is required to add three binary numbersSolution1.From the specifications of the circuit, determinethe required number of inputs and outputs andassign a letter (symbol) to each.
Full Adder (cont.)2.Derive the truth table according to the givenrelation between outputs and inputs
Full Adder (cont.)3-Obtain the simplified Boolean functions foreach output as a function of the inputvariables using K-map
Full Adder (cont.)4-Draw the logic diagram
4-Bit Binary Adder (Ripple Carry Adder)
Ripple Carry Adder
Binary Subtractor The subtraction of binary number can be donemost conveniently by means of complements The subtraction “ A-B “ is done by taking the2’s complement of “ B “ and adding it to “ A “.– The 2’s complement can be obtained by taking the1’s complement and adding “1” to the leastsignificant bit.– The 1’s complement can be implemented easilywith inverter circuit and we can add “1” to thesum by making the initial input carry of theparallel adder equal to “1”.
Adder/Subtractor
SubtractorA0011B0101D0110HALF 1100011111FULL SUBTRACTOR
Subtractor HALF SUBTRACTOR D A’B AB’ B A’B FULL SUBTRACTOR D A’B’C A’BC’ AB’C’ ABC B A’C A’B BC
4- Bit Subtractor
Assignment # 3 Design 4-Bit Adder - Subtractor
4-Bit Adder - Subtractor
Binary multiplier
Self Study 3 x 4 Bit Multiplier
Magnitude Comparator It is required to design a circuit to comparebetween two inputs A {A1,A0} and B {B1,B0}both inputs consists of two binary bits thecircuit has three outputs Greater, Less, Equal
Magnitude Comparator (cont.)1. Determine the required number of inputs andoutput.
Magnitude Comparator (cont.)2.Derive the TruthTable that defines therequired relationshipbetween inputs andoutputs.
Magnitude Comparator (cont.)3-Get the simplified logic function of theoutputs using k-map
Magnitude Comparator (cont.)4-Draw the circuit
4 – Bit Comparator
4 – Bit Comparator
An arithmetic circuit is a combinational circuit that performs arithmetic operations such as addition, subtraction, multiplication and division with binary numbers or with decimal numbers in a binary code. A combinational
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