HigherEducationandPolitics
August 23, 2023OperatingSystems
August 24, 2023ISRO CS 2020
Question 3

Minimum number of NAND gates required to implement the following binary equation
4


5


3


6

Question 3 Explanation:
ANDOR (or SOP)realization is easily convertible into NANDNAND realization.
NOTOR is equivalent to NAND.
Y = (A’+B’) (C+D)
Y = (A’+B’)C + (A’+B’)D
Let X= (A’+B’) , Y= C, and Z= D
One NAND gate is needed for implementing X= (A’ + B’).
Y= XY + XZ
Y= [(XY)’ (XZ)’]’
Three NAND gates are needed for [(XY)’ (XZ)’]’.
Total Four NAND gates are required to implement thY = (A’+B’) (C+D).
NOTOR is equivalent to NAND.
Y = (A’+B’) (C+D)
Y = (A’+B’)C + (A’+B’)D
Let X= (A’+B’) , Y= C, and Z= D
One NAND gate is needed for implementing X= (A’ + B’).
Y= XY + XZ
Y= [(XY)’ (XZ)’]’
Three NAND gates are needed for [(XY)’ (XZ)’]’.
Total Four NAND gates are required to implement thY = (A’+B’) (C+D).
Correct Answer: A
Question 3 Explanation:
ANDOR (or SOP)realization is easily convertible into NANDNAND realization.
NOTOR is equivalent to NAND.
Y = (A’+B’) (C+D)
Y = (A’+B’)C + (A’+B’)D
Let X= (A’+B’) , Y= C, and Z= D
One NAND gate is needed for implementing X= (A’ + B’).
Y= XY + XZ
Y= [(XY)’ (XZ)’]’
Three NAND gates are needed for [(XY)’ (XZ)’]’.
Total Four NAND gates are required to implement thY = (A’+B’) (C+D).
NOTOR is equivalent to NAND.
Y = (A’+B’) (C+D)
Y = (A’+B’)C + (A’+B’)D
Let X= (A’+B’) , Y= C, and Z= D
One NAND gate is needed for implementing X= (A’ + B’).
Y= XY + XZ
Y= [(XY)’ (XZ)’]’
Three NAND gates are needed for [(XY)’ (XZ)’]’.
Total Four NAND gates are required to implement thY = (A’+B’) (C+D).
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