A $C P U$ has only three instructions $I 1, I 2$ and $I 3$ , which use the following signals in time steps $T 1 - T 5 :$

$I 1 : T 1 : A i n, B o u t, C i n$
$T 2 : P C o u t, B i n$
$T 3 : Z o u t, A i n$
$T 4 : P C i n, B o u t$
$T 5 : E n d$
$I 2 : T 1 : C i n, B o u t, D i n$
$T 2 : A o u t, B i n$
$T 3 : Z o u t, A i n$
$T 4 : B i n, C o u t$
$T 5 : E n d$
$I 3 : T 1 : D i n, A o u t$
$T 2 : A i n, B o u t$
$T 3 : Z o u t, A i n$
$T 4 : D o u t, A i n$
$T 5 : E n d$

Which of the following logic functions will generate the hardwired control for the signal Ain?

(T 1 + T 2) . I 1 + (T 2 + T 4) . I 3 + T 3

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T 1. I 1 + T 2. I 3 + T 4. I 3 + T 3

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(T 1 + T 2) . I 2 + (T 1 + T 3) . I 1 + T 3

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(T 1 + T 2 + T 3) . I 3 + T 1. I 1

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Solution

The correct option is B $T 1. I 1 + T 2. I 3 + T 4. I 3 + T 3$
$W e n e e d t o f i n d h a r d w a r e c o n t r o l$
$f o r t h e s i g n a l A_{i n} :$

$I n i n s t r u c t i o n I 1 A_{i n} p r e s e n t f o r T 1$
$a n d T 3, s o T 1 I 1 + T 3 I 1$

$I n i n s t r u c t i o n I 2 A_{i n} p r e s e n t f o r T 3$
$o n l y, s o T 3 I 2$

$I n i n s t r u c t i o n I 3 A_{i n} p r e s e n t f o r T 2, T 3$
$a n d T 4, s o T 3 I 3 + T 4 I 3 + T 2 I 3$

$S o, l o g i c f u n c t i o n i s S O P f o r m i s :$

$= T 1 I 1 + T 3 I 1 + T 3 I 2 + T 3 I 3 + T 4 I 3 + T 2 I 3$
$= T 1 I 1 + T 3 (I 1 + I 2 + I 3) + T 4 I 3 + T 2 I 3$
$= T 1 I 1 + T 3 + T 4 I 3 + T 2 I 3$ $(∵ I 1 + I 2 + I 3 = 1)$

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