1. De Morgan’s laws presentation

2. De Morgan’s laws
De Morgan’s laws allow us to simplify Boolean expressions that use AND or OR. They can be summarised as:
Invert the inputs
Combine them using the ‘other’ operation
Invert the result

3. De Morgan’s laws
Law 1
————
A + B = A . B

4. De Morgan’s laws
Law 1
————
A + B = A . B
Law 2
————
A . B = A + B

5. De Morgan’s laws
To see why the first law is true, draw up a truth table: A B 1

6. De Morgan’s laws
Invert input A: __ A B 1

7. De Morgan’s laws
Invert input B: A B 1 __ __

8. A B A . B 1 De Morgan’s laws ‘AND’ the two inverted inputs …. __ __ __
__ __ A B
A . B 1 __ __

9. A B A . B 1 De Morgan’s laws …. and finally, invert again : ——— __ __
__ __
——— A B
A . B 1 __ __

10. A B A+B A . B 1 De Morgan’s laws
So the truth tables for both sides of law 1 are identical A B
A+B
A . B 1
———

11. A B 1 De Morgan’s laws The second law can be verified in the same way:1
Pause here for students to work it out on paper.

12. De Morgan’s laws
Invert input A: A B 1 __

13. De Morgan’s laws
Invert input B: A B 1 __ __

14. A B A + B 1 De Morgan’s laws ‘OR’ the two inverted inputs …. __ __ __
__ __ A B
A + B 1 __ __

15. A B A + B 1 De Morgan’s laws …. and finally, invert again : ——— __ __
__ __
——— A B
A + B 1 __ __

16. A B A . B A + B 1 De Morgan’s laws
So the truth tables for both sides of law 2 are identical A B
A . B
A + B 1
———