- Asked 2/19
- 2074 Bhadra · 8 marks
- 2078 Baisakh · 8 marks
Single-purpose processor for power
Short answer
The algorithm initializes result=1, count=0, and repeatedly multiplies result by base while count<exponent. The FSMD uses wait, init, test, multiply, and output states. Datapath includes registers for base, exponent, count, result, a multiplier, incrementer, comparator, and a mux to load initial 1 or product.
Design a single purpose processor to determine the value of x to the power n (read two integers a and b and calculate a^b, showing all the steps). Start the design from the function computing the desired result, FSMD, datapath and controller.
The processor reads integers a (base) and b (exponent, b >= 0) and computes a^b by repeated multiplication.
Step 1: Function
Power(a, b):
result = 1; count = 0
while (count < b) {
result = result * a
count = count + 1
}
output result
Step 2: FSMD
| State | Condition | Actions (RTL) | Next |
|---|---|---|---|
| S0 (wait) | start = 0 | done = 0 | S0 |
| S0 | start = 1 | load a, b into A, B | S1 |
| S1 (init) | always | R = 1, C = 0 | S2 |
| S2 (test) | C < B | none | S3 |
| S2 | C >= B | none | S4 |
| S3 (multiply) | always | R = R * A, C = C + 1 | S2 |
| S4 (output) | always | out = R, done = 1 | S0 |
S0 --start=1--> S1 (R=1,C=0) --> S2 (test C<B)
S2 --C<B-----> S3 (R=R*A, C=C+1) --> S2
S2 --C>=B----> S4 (out=R, done=1) --> S0
Step 3: Datapath
a_in -> [A] --------------+
v
+-----+ R*A +-------+
R <---| mux |<--------| * |<-- R
|(1/prod) +-------+
+-----+
b_in -> [B] --> [ C < B ] --> lt (to controller)
^
C <-- mux(0 / C+1) -+ (incrementer on C)
R --> out
Components: registers A, B, C, R; multiplier (R x A); incrementer (C + 1); comparator (C < B); mux for R (1 or product) and C (0 or C + 1).
Controller
State register (3 bits) with inputs start and lt (C < B). Outputs: loadA, loadB, R_sel/R_load, C_clr/C_inc, out_en, done. 5-state FSM as in the table.
Trace: a = 2, b = 3: R = 1; C = 0 -> R = 2, C = 1 -> R = 4, C = 2 -> R = 8, C = 3 -> stop, output 8.
✓ Answer checked by Claude Opus 5.5 (high effort)
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