Using De’Morgan’s On of the most useful principles in boolean algebra is De’Morgan’s...
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Transcript of Using De’Morgan’s On of the most useful principles in boolean algebra is De’Morgan’s...
Using De’Morgan’s
• On of the most useful principles in boolean algebra is De’Morgan’s Theorem, which allows one to switch between ANDs and NORs and ORs and NANDs.
• NOT terms or Inverted terms are represented with a line over the terms
• AB = A + B
• A + B = AB
To convert A+B into a form that can be implemented using a NAND gate follow these steps:
• 1. Double Complement the term A+B = A+B
• 2. Use DeMorgan’s to distribute one of the complements
A+B = A B
The equation is now a NAND of the complemented inputs.
To convert AB into a form that can be implemented using a NOR gate follow these steps:
• 1. Double Complement the term AB = AB
• 2. Use DeMorgan’s to distribute one of the complements
AB = A + B
The equation is now a NOR of the complemented inputs.
A B Output
0 0 0
0 1 1
1 0 0 Out = A B
1 1 0 DoubleC A B
DeM A + B
Simplify A + B
Exercise 1
A B C Output
0 0 0 1
0 0 1 0
0 1 0 0 Out = A B C + A B C
0 1 1 0 DoubleC A B C + A B C
1 0 0 0 DeM (A B C) ( A B C)
1 0 1 0
1 1 0 1
1 1 1 0
1.Draw a gate diagram that implements this function in three NAND gates plus invertors. Your diagram will have two levels of NAND gates.
Exercise 2
1. Build a truth table for the following problem: PC power/security.
A computer needs to be secured from un-authorized access in the following way: The power should only come on when
A. The security key is present in the lock
B. The case cover is closed
C. The user presses the power-on button.
2. Use DeMorgan’s and boolean algebra to convert a function extracted from your truth table above, into one that can be constructed with either NANDs or NORs.
3. Draw a circuit diagram with gates that implements your function from step 2.