The Islamic University of Gaza Engineering Faculty Department of Computer Engineering Fall 2017 ECOM 2013 Lamia Z. Shu'shaa Khaleel I. Shaheen Combinational Digital Design Laboratory Manual Experiment #1 Basic Logic Functions & Gates Objectives • To study Basic logic gates: INV, AND, OR, NAND, NOR, XOR, XNOR • To study Logic Diagrams, Boolean Functions, Truth Tables and Boolean algebra of these gates. Prelab Use Logisim Software to simulate the functions of the basic gates as shown in figures below. Theoretical Background 1. Inverter Gate (NOT) • Logic Diagram • Truth Table • Boolean Expression F = A' • 2 Pin Diagram Input Output 0 1 1 0 2. AND Gate • Logic Diagram • Truth Table • Input1 Input2 Output 0 0 0 0 1 0 1 0 0 1 1 1 Boolean Expression F = AB = A . B • Pin Diagram 3. OR Gate • 3 Logic Diagram • • Truth Table Input1 Input2 Output 0 0 0 0 1 1 1 0 1 1 1 1 Input1 Input2 Output 0 0 1 0 1 1 1 0 1 1 1 0 Boolean Expression F=A+B • Pin Diagram 4. NAND Gate 4 • Logic Diagram • Truth Table • Boolean Expression F = (AB)' = A' + B' • Pin Diagram 5. NOR Gate • Logic Diagram • Truth Table • Input1 Input2 Output 0 0 1 0 1 0 1 0 0 1 1 0 Boolean Expression F = (A + B)' = A'B' • 5 Pin Diagram 6. XOR Gate • Logic Diagram • Truth Table • Input1 Input2 Output 0 0 0 0 1 1 1 0 1 1 1 0 Boolean Expression F = A B = A'B + AB' • 6 Pin Diagram 7. XNOR Gate • Logic Diagram • Truth Table • Input1 Input2 Output 0 0 1 0 1 0 1 0 0 1 1 1 Boolean Expression F = (A B)' = (A + B')(A' + B) Examples on Boolean Algebra Example 1: Using Logisim, draw a circuit that uses basic logic gates to realize the following function F = AB' + C Solution: 7 Example 2: Write Boolean expression describing the output of the circuit described by the logic diagram in the Figure below Solution: F = (AB + C)' D DE Morgan's Theorem 8 • (XY)' = X' + Y' • (X + Y)' = X'Y' • Truth Table for DE Morgan's Theorem: X Y X' Y' X+Y (X + Y)' X'Y' XY (XY)' X' + Y' 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 Lab Work Equipment’s required: • KL-31001 trainer kit. • IC's 74LS04 (Hexa NOT), 74LS08 (Quad 2 input AND), 74LS32 (Quad 2 input OR). • The Datasheets of the IC’s. Basic Gates • Connect the 74LS08 to the breadboard, connect +5V to pin 14 and 0V (ground) to pin 7, connect one AND gate inputs to data switches, SW1 and SW2 TTL level and output to LED L0 of the trainer kit, and record down its truth table. • Repeat previous part for all other gates. Exercises 1. Using Logisim, draw logic diagram for the following expression: u + w(xyz)' 2. Write Boolean expression and construct the truth table describing the output of the circuit described by the logic diagram in the Figure below. 9