# GATE - 2004 | OS | A CPU has only three instructions I1, I2 and I3, which use the

## Question:

A CPU has only three instructions I1, I2 and I3, which use the following signals in time steps T1-T5:

I1 : T1 : Ain, Bout, Cin
T2 : PCout, Bin
T3 : Zout, Ain
T4 : Bin, Cout
T5 : End

I2 : T1 : Cin, Bout, Din
T2 : Aout, Bin
T3 : Zout, Ain
T4 : Bin, Cout
T5 : End

I3 : T1 : Din, Aout
T2 : Ain, Bout
T3 : Zout, Ain
T4 : Dout, Ain
T5 : End

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

 A T1.I1 + T2.I3 + T4.I3 + T3 B (T1 + T2 + T3).I3 + T1.I1 C (T1 + T2 ).I1 + (T2 + T4).I3 + T3 D (T1 + T2 ).I2 + (T1 + T3).I1 + T3

## Solution:

### Option (A) is Correct.

We just have to see which option gives 1 whenever Ain is 1 and 0 otherwise.
So, Ain is 1 in T3 of I1, I2 and I3. Also during T1, and T2 and T4 of I3.

T1.I1 + T2.I3 + T4.I3 + T3.I1 + T3.I2 + T3.I3

Since, CPU is having only 3 instructions, T3.I1 + T3.I2 + T3.I3 can be replaced by T3.

So, T1.I1 + T2.I3 + T4.I3 + T3

Thank You