Company LOGO DKT 122/3 DIGITAL SYSTEM 1 WEEK #7 COMBINATIONAL LOGIC ANALYSIS

Topic Outlines  Basic Combinational Logic Circuits  Implementing Combinational Logic  Implement Logic Circuit from Boolean Expression  Implement Logic Circuit from Truth Table  The Universal Property of NAND and NOR Gates  NAND Gate as a Universal Logic Element  NOR Gate as a Universal Logic Element  Combinational Logic Using NAND and NOR Gates  Logic Circuits Operations with Pulse Waveform Inputs

Basic Combinational Logic Ccts DEFINITION OF COMBINATIONAL LOGIC  Combination of basic gates to form circuits that can carry out a desired application.  In combinational logic, the output level is at all times dependent on the combination of input levels  Combinational logic circuits contain no memory (no ability to store information)

Basic Combinational Logic Ccts AND-OR LOGIC Represents SOP implementation – AND gate for product term, OR gate for summing the product terms

AND-OR-INVERT LOGIC Represents POS implementation – AND gate for product term, OR gate for summing the product terms, NOT gate to complement the AND-OR circuit. Basic Combinational Logic Ccts

XOR LOGIC Combination of 2 AND gates, 1 OR gate, & 2 NOT gates. Considered a type of logic with own unique symbol ( ).

Basic Combinational Logic Ccts XNOR LOGIC The complement of XOR logic.

Implementing Combinational Logic Example: Logic circuit for X = AB + CDE Implement logic circuit from Boolean Expression

Example: Logic circuit for X = AB(CD + EF) It is usually best to reduce a circuit to SOP form to reduce the overall propagation delay time. Implement logic circuit from Boolean Expression Implementing Combinational Logic

First, write the SOP expression from the Truth Table. Then, implement the logic circuit. INPUTOUTPU T ABCX QUESTION: What is the SOP expression? QUESTION: What is the SOP expression? Implementing Combinational Logic Implement logic circuit from Truth-table

Universal Property - NAND & NOR NAND gate is a universal gate because it can be used to produce the NOT, AND, OR and NOR functions. NAND GATE AS A UNIVERSAL LOGIC ELEMENT

Universal Property - NAND & NOR NAND GATE AS A UNIVERSAL LOGIC ELEMENT (Cont.)

NOR gate is also a universal gate because it can be used to produce the NOT, AND, OR and NAND functions. Universal Property - NAND & NOR NOR GATE AS A UNIVERSAL LOGIC ELEMENT

Universal Property - NAND & NOR NOR GATE AS A UNIVERSAL LOGIC ELEMENT (Cont.)

Combinational Logic - NAND & NOR NAND Gate can function as either a NAND or a negative-OR because by DeMorgan’s Theorem: AB = A + B NANDNegative-OR The NAND symbol and the negative-OR symbol are called dual- symbol. NAND LOGIC

NOR Gate can function as either a NOR or a negative-AND because by DeMorgan’s Theorem: A+ B = A B NORNegative-AND The NOR symbol and the negative-AND symbol are called dual- symbol. Combinational Logic - NAND & NOR NOR LOGIC

Example: Using appropriate dual symbols, redraw the logic diagram and develop the output expression for the following circuit: Combinational Logic - NAND & NOR

Pulse Waveform Inputs Operation The output of a logic circuit at any given time depends on the input at that particular time. Example: Determine the final output waveform X for the circuit in figure below, with input waveforms A,B and C as shown. END