Page 97 - Computer Science V2.0 Class 11

Ans. The resultant SOP expression is:
U'VW' + U'VW + UV'W' + UVW

Case-based Questions

1. Srikeerti is new to logic gates. She wants to create a ready reckoner, in the form of a table, for herself so that she can refer
to the same whenever she is studying Boolean algebra. Help her complete the task.

Sr No Name of gate Symbol Example Boolean Expression
1 AND A.B
2 OR A+B
3 NOT A'

4 XOR

5 NAND

Ans.

Sr No Name of gate Symbol Resultant Boolean Expression
1 AND A.B

2 OR A+B

3 NOT A'

4 XOR A XOR B = AB' + BA'

5 NAND (A●B)'

2. Ramya is learning about logic gates. Her friend tells her that out of all gates, NOR and NAND are called fundamental gates.
But he could not explain to her any reason for the same. Do you know why NAND and NOR are called universal gates?
Explain to Ramya using Boolean expressions and using a logic circuit for AND gate.
Ans. NAND and NOR are called universal gates because all other gates can be implemented using these gates. For example, an
AND gate can be implemented using NAND gates, as shown below:
AND gate: A ● B = ((A ●B)')' = ((A ● B)' ● (A ● B)')'
= ((A NAND B) NAND (A NAND B)
Logic Circuit using NAND gate

A

B

Also, A●B = ( (A+A)' + (B+B)' )'
= (A NOR A) NOR (B NOR B)
Logic Circuit using NOR gate

Boolean Logic 83