A CPU has only three instructions I1, I2 and I3, which use the following…
2004
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
Attempted by 61 students.
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Correct answer: A
Answer: Ain = T1·I1 + T2·I3 + T4·I3 + T3
Derivation:
Examine when Ain is asserted for each instruction.
Instruction I1: Ain is active at T1 and at T3.
Instruction I2: Ain is active at T3 only.
Instruction I3: Ain is active at T2, T3 and T4.
Since T3 asserts Ain for all instructions, include T3 as a standalone term. Add specific instruction-time terms for the remaining asserts: T1·I1, T2·I3 and T4·I3.
Combine terms to get Ain = T1·I1 + T2·I3 + T4·I3 + T3. This can be written equivalently as Ain = T3 + T1·I1 + (T2 + T4)·I3.