1. Combinational Logic Digital Design Department of Software Development Faculty of Information Technology Islamic University of Gaza Dr. Rebhi Baraka rbaraka@iugaza.edu

2. Basic Combinational Logic Circuits AND-OR LogicAND-OR Logic AND-OR-Invert LogicAND-OR-Invert Logic Exclusive-OR LogicExclusive-OR Logic

3. Basic Combinational Logic Circuits AND-OR LogicAND-OR Logic

4. Basic Combinational Logic Circuits AND-OR Invert LogicAND-OR Invert Logic

5. Basic Combinational Logic Circuits Exclusive-OR LogicExclusive-OR Logic

6. Basic Combinational Logic Circuits Exclusive-NOR LogicExclusive-NOR Logic

7. Implementing Combinational Logic Implementing Combinational Logic From Boolean expression to logic circuitFrom Boolean expression to logic circuit –Given a Boolean expression, create a logic circuit that implements that expression. From truth table to logic circuitFrom truth table to logic circuit –Given a truth table, create a logic circuit that implements that table.

8. Implementing Combinational Logic Implementing Combinational Logic From Boolean expression to logic circuitFrom Boolean expression to logic circuit Logic circuit for X = AB + CDE.

9. Implementing Combinational Logic Implementing Combinational Logic Implement the following Boolean expression:Implement the following Boolean expression:

10. Implementing Combinational Logic Implementing Combinational Logic From truth table to logic circuitFrom truth table to logic circuit –Given a truth table, create a logic circuit that implements that table. OutputInput XCBA A’BC AB’C’ 0001100000011000 0101010101010101 0011001100110011 0000111100001111 The SOP expression obtained from the truth table is

11. Implementing Combinational Logic Implementing Combinational Logic From truth table to logic circuit (continued)From truth table to logic circuit (continued)

12. Implementing Combinational Logic Implementing Combinational Logic Example: Design a logic circuit to implement the operation specified in the truth tableExample: Design a logic circuit to implement the operation specified in the truth table OutputInput XCBA A’BC AB’C ABC’ 0001011000010110 0101010101010101 0011001100110011 0000111100001111

13. Implementing Combinational Logic Implementing Combinational Logic Example: Design a logic circuit with 4 inputs that will only produce a 1 output when exactly 3 inputs are 1s.Example: Design a logic circuit with 4 inputs that will only produce a 1 output when exactly 3 inputs are 1s. The combinations in which there are exactly 3 1s are listed in the table with their product terms DCBA A’BCD AB’CD ABC’D ABCD’ 11101110 11011101 10111011 01110111 X = A’BCD + AB’CD + ABC’D + ABCD’

14. The Universal Property of NAND and NOR Gates NAND and NOR gates are “universal” because they can be used to produce any of the other logic functions.

15. The Universal Property of NAND Gates

16. The Universal Property of NOR Gates

17. These slides are based on Digital Fundamentals 9 th ed. By Thomas Floyd