Machines with Memory - Models of Computation: Exploring the Power of Computing - page 108

Input Encoding
σ

Output Encoding
λ ( q )

State Encoding
q cs
q 0 00
q 1 01
q 2 10
q 3 11

Σ uv
0000
0101
1010
1111

∈ ∈ λ ( q )

Ψ

0 0

1 1

B 2
csuvc ∗ s ∗
000000
010000
100001
110001
000101
010101
100110
110110
001001
011001
101010
111010
001110
011110
101111
111111

δ : B 4 λ : B 2 → B

c ∗ s ∗ s
000
011
100
111

→

Figure 3.14 Encodings for inputs, outputs, states, and the next-state and output functions of
the FSM adder.

c

c ∗

M

s ∗

s

M

g

Clock

p

u v

Figure 3.15 A sequential circuit for the FSM that adds binary numbers.