Description
PART I (9 POINTS)
Assume that X consists of 2 bits, x1 and x0, and Y consists of 2 bits, y1 and y0. Write logic
functions that are true if and only if
(A) X <Y, where X and Y are thought of as unsigned binary numbers
(B) X <Y, where X and Y are thought of as signed (two’s complement) numbers
(C) X = Y
PART II (12 POINTS)
Describe the effect that a single stuck-at-0 fault (i.e., regardless of what it should be, the signal is
always 0) would have for the signals shown below, in the single-cycle datapath (shown in the
figure in Part IV). Which instructions (R-type, lw, sw, or beq), if any, will not work correctly?
Explain why.
Consider each of the following faults separately:
A) RegWrite = 0
B) ALUOp0 = 0
C) ALUOp1 = 0
D) Branch = 0
E) MemRead = 0
F) MemWrite = 0
PART III (12 POINTS)
This exercise is similar to Part II, but this time consider stuck-at-1 faults. Describe the effect that
a single stuck-at-1 fault (i.e., regardless of what it should be, the signal is always 1) would have
for the signals shown below, in the single-cycle datapath (shown in the figure in Part IV). Which
instructions (R-type, lw, sw, or beq), if any, will not work correctly? Explain why.
Consider each of the following faults separately:
A) RegWrite = 1
B) ALUOp0 = 1
C) ALUOp1 = 1
D) Branch = 1
E) MemRead = 1
F) MemWrite = 1
PART IV (7 POINTS)
We wish to add the instructions jr (jump register) to the single-cycle datapath described in the
lectures. Add any necessary datapaths and control signals to the single-cycle datapath shown in
the Figure below. Then fill the table that demonstrates the setting of the control lines.
