De Morgan’s laws presentation

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Presentation transcript:

De Morgan’s laws presentation

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

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

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

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

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

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

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

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

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 ———

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.

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

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

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

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

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 ———