Page 36 - Handout Digital Electronics

T10 De Morgan’s theorem

a) A + B = A.B
b) AB = A + B

Worked examples

Use postulates to show that:

A + AB = A + B

= A • 1 + AB = A + B

= A(1 + B) + AB = A + B

= A + AB + AB = A + B

= A + B( A + A) = A + B
= A + B = A + B

Show that:

A + AC = A + C

= A • 1 + AC = A + C

= A(1 + C ) + AC = A + C

= A + AC + AC = A + C

= A + C ( A + A) = A + C

= A + C = A + C

Show that:

( A + B)( A + C) = A + BC
= A • A + A • C + B • A + B • C = A + BC
= A + AC + AB + BC = A + BC
= A(1 + C) + AB + BC = A + BC

= A + AB + BC = A + BC
= A(1 + B) + BC = A + BC
= A + BC = A + BC

36