Company LOGO DKT 1223 DIGITAL SYSTEM 1 WEEK

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

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

Basic Combinational Logic Ccts DEFINITION OF COMBINATIONAL LOGIC Ü Combination of basic gates to form circuits that can carry out a desired application. Ü In combinational logic, the output level is at all times dependent on the combination of input levels Ü 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

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

Implementing Combinational Logic 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.

Implementing Combinational Logic Implement logic circuit from Truth-table First, write the SOP expression from the Truth Table. Then, implement the logic circuit. INPUT OUTPUT A B C X 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 QUESTION: What is the SOP expression?

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

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

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

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

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

Combinational Logic - NAND & NOR 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. E D N