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  4. A combination of logic gates has the truth table shown below: P Q Z 0 0 0 0 1 1 1 0 1 1 1 1 Which combination has this table?

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Q. A combination of logic gates has the truth table shown below:
$P$ $Q$ $Z$
0 0 0
0 1 1
1 0 1
1 1 1

Which combination has this table?

Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

(a) $Z=\overline{\bar{P} . Q}=P+\bar{Q}$
(b) $Z=(\overline{\overline{P+Q}). \bar{Q}}=(\overline{\overline{P+Q}})+Q$
$=P+Q+Q=P+Q$
(c) $Z=\overline{(\overline{P. Q}) .\bar{Q}}=(\overline{\overline{P . Q}})+\bar{\bar{Q}}=P .Q+Q=Q$
(d) $Z =P.Q$
From given truth table,
$Z =\bar{P} Q+P \bar{Q}+P Q=Q(P+\bar{P})$
$+P \bar{Q}=Q P+P \bar{Q}=P Q$
So, the truth table and combination of gates in option
(d) performs AND operation.