IMPLEMENTATION OF BOOLEAN EXPRESSION AND LOGIC FUNCTION USING ONLY NAND GATES

Here, the Step by Step process of realization or implementation of Boolean expressions or logic functions using only NAND Gates, which is an universal gate, is shown with the help of various examples.

IMPLEMENTATION OF BOOLEAN EXPRESSION AND LOGIC FUNCTION USING ONLY NAND GATES

Example-1:. Implement Boolean expression Y = AB + CD using only NAND gates.

Solution: Y = AB + CD

Step-1: Take double bar on both sides of the above expression

Step-2: Apply De Morgan’s Theorem to the inner bar of the right side of the above expression

Step-3: The above expression can easily be implemented using NAND GATES as shown in Fig. 1:

Example-2: Implement logic function F(A, B, C, D) = Σm (0, 1, 4, 5, 6, 7, 8, 9, 12, 13, 14) using NAND gates.

Solution: To implement a logic function using only NAND gates, the function is to be written in SOP (Sum of Product) form.

Using K-Map the logic function F(A, B, C, D) = Σm (0, 1, 4, 5, 6, 7, 8, 9, 12, 13, 14) is simplified and written in SOP form as given below:

Boolean Expression of the given logic function in SOP form would be

Now, take double bar on both sides of the above expression

The above expression can easily be implemented using NAND GATES as shown in Fig. 2:

Fig. 2

Example-3: Implement F(A, B, C, D) = ΠM (0, 1, 3, 5, 6, 7, 11, 13, 14) using NAND gates.

Solution: Here maxterms are given in the logic function. Using maxterms POS (Product of Sum) expression can be formed. But to implement a circuit using NAND Gates an expression in SOP form is needed.

So, convert the given logic function, F(A, B, C, D) = ΠM (0, 1, 3, 5, 6, 7, 11, 13, 14), in minterm form.

i.e., F(A, B, C, D) = Σm (2, 4, 8, 9, 10, 12, 15)

Then write the simplified Boolean expression in SOP form using K-Map and follow all the three steps discussed in Example-1.

 

Hope this post on "IMPLEMENTATION OF BOOLEAN EXPRESSION AND LOGIC FUNCTION USING ONLY NAND GATES" would be helpful to gain knowledge on how to implement any digital circuit using NAND Gates only.

Related Link:

• REALIZATION OF BOOLEAN EXPRESSIONS AND LOGIC FUNCTIONS USING ONLY NOR GATES

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• Flip-flop Conversion – SR flip-flop to JK flip-flop
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• Flip-flop Conversion – JK flip-flop to D flip-flop
• Flip-flop Conversion – D flip-flop to SR flip-flop
• Flip-flop Conversion – JK flip-flop to SR flip-flop
• Flip-flop Conversion – JK flip-flop to T flip-flop
• Flip-flop Conversion – T flip-flop to D flip-flop
• Flip-flop Conversion – T flip-flop to SR flip-flop
• Flip flop Conversion – D flip-flop to T flip-flop
• Flip flop Conversion – SR flip-flop to T flip-flop
• Flip flop Conversion – T flip-flop to JK flip-flop
• Flip flop Conversion – D flip-flop to JK flip-flop