Design Of Combinational Logic Circuits

1. Design Of Combinational Logic Circuits Digital Circuit Design

2. Design of combinational digital circuits • Steps to design a combinational digital circuit: • From the problem statement derive the truth table • From the truth table derive the unsimplified logic expression • Simplify the logic expression • From the simplified expression draw the logic circuit • Example: Design a 3-input (A,B,C) digital circuit that will give at its output (X) a logic 1 only if the binary number formed at the input has more ones than zeros. Digital Circuit Design

3. Design of combinational digital circuits (Cont.) • Example: Design a 4-input (A,B,C,D) digital circuit that will give at its output (X) a logic 1 only if the binary number formed at the input is between 2 and 9 (including). Digital Circuit Design

4. Design of combinational digital circuits (Cont.) • Example: Design a 4-input (A,B,C,D) digital circuit that will give at its output (X) a logic 1 only if the binary number formed by the inputs (AB) is greater or equal to the binary number formed by the inputs (CD). Digital Circuit Design

5. Tutorial: Design a 4-input (A,B,C,D) digital circuit that will give at its output a binary number equal to the sum of the binary numbers formed by the inputs (AB) and (CD). Digital Circuit Design

6. Digital Circuit Design

7. Tutorial: Design a 4-input (A,B,C,D) digital circuit that will give at the output: • X a logic 1 if the binary number formed by the inputs (AB) is greater than (CD). • Y a logic 1 if the binary number formed by the inputs (AB) is less than (CD). • Z a logic 1 if the binary number formed by the inputs (AB) is equal to (CD). Digital Circuit Design

8. Digital Circuit Design

9. Homework: Design a 4-input (A,B,C,D) digital circuit that will give at the output: • X a logic 1 if in the binary number formed at the inputs there are more zeros than ones. • Y a logic 1 if in the binary number formed at the inputs there are less zeros than ones. • Z a logic 1 if in the binary number formed at the inputs there equal zeros and ones. Digital Circuit Design

10. Digital Circuit Design

11. Homework: Design a 4-input (A,B,C,D) digital circuit that will give at its output a binary number equal to the product of the binary numbers formed by the inputs (AB) and (CD). Digital Circuit Design

12. Digital Circuit Design

13. Don’t Care Conditions • In many application it is known in advance that some of the input combinations will never occur. These combinations are marked as “Don’t Care Conditions” and are used as either zero’s or one’s so that the application is implemented with the most simplified circuit. • Example: Simplify the logic expression X(A,B,C,D) with the don’t care conditions d(A,B,C,D). Digital Circuit Design

14. Don’t Care Conditions: Examples Digital Circuit Design

15. Homework: Design a digital circuit that has as input a 1-digit Binary Coded Decimal (BCD) number. The circuit must give at its output a binary number equal to the absolute value of (2M – 5), where M is the number formed at the input. Digital Circuit Design

16. Digital Circuit Design

17. Digital Circuit Design

18. Digital Circuit Design