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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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