Exercise 4.8 When silicon chips are fabricated, defects in materials (e.g., silicon) and manufacturing errors can result in defective circuits. A very common defect is for one wire to affect the signal in another. This is called a cross-talk fault. A special class of cross-talk faults is when a signal is connected to a wire that has a constant logical value (e.g., a power supply wire). In this case we have a stuck-at-0 or a stuckat-
1 fault, and the affected signal always has a logical value of 0 or 1, respectively.
The following problems refer to the following signal from Figure 4.24:
Signal

a. Instruction Memory, output Instruction, bit 7

b. Control unit, output MemtoReg 4.8.1 [10] <4.3, 4.4> Let us assume that processor testing is done by fi lling the PC, registers, and data and instruction memories with some values (you can choose which values), letting a single instruction execute, then reading the PC, memories, and registers. These values are then examined to determine if a particular fault is present. Can you design a test (values for PC, memories, and registers) that would determine if there is a stuck-at-0 fault on this signal?
4.8.2 [10] <4.3, 4.4> Repeat Exercise 4.8.1 for a stuck-at-1 fault. Can you use a single test for both stuck-at-0 and stuck-at-1? If yes, explain how; if no, explain why not.
4.8.3 [60] <4.3, 4.4> If we know that the processor has a stuck-at-1 fault on this signal, is the processor still usable? To be usable, we must be able to convert any program that executes on a normal MIPS processor into a program that works on this processor. You can assume that there is enough free instruction memory and data memory to let you make the program longer and store additional data. Hint:
the processor is usable if every instruction “broken” by this fault can be replaced with a sequence of “working” instructions that achieve the same effect.
The following problems refer to the following fault:
Fault

a. Stuck-at-1

b. Becomes 0 if Instruction [31-26] has all bits at 0, no fault otherwise 4.8.4 [10] <4.3, 4.4> Repeat Exercise 4.8.1, but now the fault to test for is whether the “MemRead” control signal has this fault.
4.8.5 [10] <4.3, 4.4> Repeat Exercise 4.8.1, but now the fault to test for is whether the “Jump” control signal has this fault.

4.8.6 [40] <4.3, 4.4> Using a single test described Exercise 4.8.1, we can test for faults in several different signals, but typically not all of them. Describe a series of tests to look for this fault in all Mux outputs (every output bit from each of the fi ve Muxes)? Try to do this with as few single-instruction tests as possible.