Find. The physical address in each case (or the appropriate error if the logical address is invalid).
Approach. A base/limit (relocation) MMU accepts a logical address only if $0\le \text{logical} \lt \text{limit}$; if valid, physical $=$ base $+$ logical, otherwise the CPU traps an addressing error and no physical address is generated.
(a) Check bounds, then translate. $501 \lt 1500$ (the limit), so the address is valid.
$$\text{physical} = \text{base}+\text{logical} = 1300+501=\boxed{1801}$$
(b) Check bounds first. $1550 \ge 1500$ (the limit) — the logical address lies outside the process's address space.
$$\boxed{\text{Addressing error trap: no physical address is generated (1550} \ge \text{limit 1500)}}$$
This case exists specifically to test that the limit check, not just the addition, must be applied — the base value (1600) is a distractor.
Approach. Simulate FIFO: maintain a queue of resident pages; a reference already resident is a hit; otherwise it's a fault, and if the frames are full, evict the oldest-loaded page (front of the queue) before loading the new one.
Step through the reference string, tracking the 3 resident frames in load order.
FIFO trace, 3 frames
Ref
92
93
94
95
93
94
91
96
97
99
97
99
99
97
99
91
Fault?
F
F
F
F
hit
hit
F
F
F
F
hit
hit
hit
hit
hit
F
Frames
92
92,93
92,93,94
93,94,95
93,94,95
93,94,95
94,95,91
95,91,96
91,96,97
96,97,99
96,97,99
96,97,99
96,97,99
96,97,99
96,97,99
97,99,91
Each fault (F) is counted once; the table shows the resident set (in load order, oldest first) after each reference.
Count the faults. Faults occur at references 92, 93, 94, 95, 91, 96, 97, 99, 91 (the last one) — nine references marked "F" in the trace.
$$\boxed{\text{FIFO page faults (3 frames)} = 9}$$
Final Results – Question 2(c)
Quantity
Value
Reference string length
16
Frames
3
Page faults (FIFO)
9
Hits
7
(d) Hard vs. soft real-time classification
(i) An airline reservation system is a soft real-time system: it should respond promptly, but an occasional slow response degrades user experience and may cost business, it does not endanger life or cause catastrophic failure. (ii) A spaceship direction control system is a hard real-time system: a missed deadline in attitude/thruster control can mean loss of the vehicle or crew, so every control-loop deadline must be met without exception.
