# Help with DeMorgans Laws

Discussion in 'Homework Help' started by hdnixon, Dec 6, 2006.

1. ### hdnixon Thread Starter New Member

Dec 6, 2006
1
0
Hi Guys,

Im struggling to convert a circuit from using OR & AND gates to one that only uses NOR gates. Basically its a car alarm. S is the SET function on an alarm and A,B,C are three sensors. Ive worked out that the complete function for my circuit is S.(A+B+C) ... should read S AND (A OR B OR C)

Heres my circuit...

Ive used crocodile clips to prove that my circuit works and to create the second circuit using only NOR gates (By trial and error) but now i have to rearrange my original formula using DeMorgans laws.

Can anyone help me

2. ### Dave Retired Moderator

Nov 17, 2003
6,960
145
To allow you to use Demorgan's Theorum you need to put two NOT gates at the output of the AND gate IC1a (to keep the circuit function the same), so your function is:

NOT(NOT(S AND (A OR B OR C))

Using Demorgan's this gives:

NOT(NOT(S) OR NOT(A OR B OR C))

The identity you require is: NOT(A AND B) = NOT(A) OR NOT(B) (reference here)

Use a NOR gate for the NOT(S) but tie the inputs together no that it operates as a NOT gate, and use a three input NOR gate for (A OR B OR C). Finally place a NOR gate at the output with the inputs fed from NOT(S) and NOT(A OR B OR C).

This gives you the second circuit you have drawn.

Dave

3. ### cell1987 New Member

Nov 30, 2006
7
0
is there any way to simplfy this equation?i have to implement it only using NOR gates.

f=a'b'c'+a'bc+ab'c+abc'