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Bask 2
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NAND and NOR Implementations
(Gncellenme Tarihi: 30.10.2012)
NAND Implementation
Algebraic Method
1. Obtain the Boolean function Fin the sum-of-products form.2. Take its complement by applying DeMorgans theorem to obtain Fin the form of product of
complemented products.
3. Take the whole expression into a primed parenthesis to obtain F. Hence, the function becomessuitable for the NAND implementation.
Example 1: Implement the Boolean function F = xy + xy +z with NAND gates.
Step 1: The Boolean function F = xy + xy +z is given in the sum-of-products form.
Step 2: F = (xy+xy+z) = (xy).(xy).z
Step 3: F= [(xy).(xy).z]
Note: A three-input NAND gate can be implemented with two-input NAND gates as follows:
Graphical Method
1. Group 1s on the Karnough map.2. Obtain the simplified Boolean function in the sum-of-products form.3. Draw the logic diagram with AND and OR gates.4. Insert a bubble at the output of each AND gate and at each input of the OR gates.5. Replace INVERT-OR gates with NAND gates.
6. Check all bubbles in the logic diagram. For every bubble that is not compensated by another bubblealong the same line, insert an inverter (a one-input NAND gate) or complement the input literal.
Example 2: Implement the Boolean function F = xy + xy +z with NAND gates.
INVERT-OR gate NAND gate
AND-OR implementation INVERT-OR implementation NAND implementation
xy
Fxy
z
xy
Fxy
z
xy
F
(xy)
xy
z
(xy)
z
(x.y.z)xy
(x.y) (x.y)x
yz
(x.y.z)
xy
F
(xy)
xy
z
(xy)
xy
(xy)
xy
z
(xy)F= [(xy).(xy).z]
(xy).(xy)
[(xy).(xy)]
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