# CS 140 Lecture 10 Sequential Networks: Implementation Professor CK Cheng CSE Dept. UC San Diego 1.

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CS 140 Lecture 10 Sequential Networks: Implementation Professor CK Cheng CSE Dept. UC San Diego 1

Implementation Format and Tool Procedure Excitation Tables Example 2

Canonical Form: Mealy and Moore Machines Combinational Logic x(t) y(t) CLK C2 C1 y(t) CLK x(t) C1C2 CLK x(t) y(t) 3

Mealy Machine: y i (t) = f i (X(t), S(t)) Moore Machine: y i (t) = f i (S(t)) s i (t+1) = g i (X(t), S(t)) C1C2 CLK x(t) y(t) Mealy Machine C1C2 CLK x(t) y(t) Moore Machine s(t) Canonical Form: Mealy and Moore Machines 4

C1C2 CLK x(t) y(t) Sequential Network Implementation: Format and Tool Canonical Form: Mealy & Moore machines State Table  Netlist Tool: Excitation Table s(t) D(t) = h(x(t), S(t)) y(t) = f(x(t), S(t)) 5

Implementation: Procedure State Table => Excitation Table Given a state table Input PS x Q(t) NS, y we have NS = Q(t+1) = h(x(t),Q(t)) Output y(t) = f(x(t),Q(t)). We want to express D(t), T(t), S(t), R(t), J(t), K(t) as a funciton of inputs X(t) and current state Q(t). We derive the implementation of D, T, S, R, J, K as combinational logic. 6

Implementation: Procedure State Table: y(t) = f(Q(t), x(t)) Q(t+1) = h(x(t),Q(t)) Excitation Table: »D(t) = e D (Q(t+1), Q(t)); »T(t) = e T (Q(t+1), Q(t)); »S, R, J, K From 1 & 2, we derive »D(t) = g D (Q(t), x(t))= e D (h(x(t),Q(t)), Q(t)); »T(t) = g T (Q(t), x(t))=e T (h(x(t),Q(t)),Q(t)); »S,R,J,K. Use K-Map to derive optional combinational logic implementation. –T(t) = g T (Q(t), x(t)) –y(t) = f(Q(t), x(t)) 7

State table of a JK flip flop: 00 0 1 01 0 10 1 11 1 0 0101 Q(t) Q(t+1) JK Excitation table for a JK F-F : 0 0- 1 1- -0 0101 PS NS Q(t) Q(t+1) JK If Q(t) is 1, and Q(t+1) is 0, then JK needs to be 0-. Excitation Table 8

Excitation Tables and State Tables 0 0- 01 1 10 -0 0101 PS NS Q(t) Q(t+1) SR Excitation Tables: 0 1 0 0101 PS NS Q(t) Q(t+1) T 00 0 1 01 0 0101 PS SR Q(t) Q(t+1) SR 10 1 11 - 0 1 0 0101 PS T Q(t) Q(t+1) T State Tables: 9

0 0- 1 1- -0 0101 PS NS Q(t) Q(t+1) JK Excitation Tables: 0 1 0101 PS NS Q(t) Q(t+1) D 00 0 1 01 0 0101 PS JK Q(t) Q(t+1) JK 10 1 11 1 0 1 0101 PS D Q(t) Q(t+1) D State Tables: Excitation Tables and State Tables 10

Implementation: Example Implement a JK F-F with a T F-F 00 0 1 01 0 0101 PS JK Q(t) Q(t+1) = h(J(t),K(t),Q(t)) = J(t)Q(t)+K(t)Q(t) JK 10 1 11 1 0 State Table Q Q’ C1 J K T 11

id 0 1 2 3 4 5 6 7 J(t) 0 1 K(t) 0 1 0 1 Q(t) 0 1 0 1 0 1 0 1 Q(t+1) 0 1 0 1 0 T(t) 0 1 0 1 0 1 0 0101 PS NS Q(t) Q(t+1) Excitation Table of T flip-FlopT(t) = Q(t) XOR Q(t+1) T(t) = Q(t) XOR ( J(t)Q’(t) + K’(t)Q(t)) Excitation Table of the Design Example: Implement a JK flip-flip using a T flip-flop T 12

0 2 6 4 1 3 7 5 Q(t) J 0 0 1 1 0 1 1 0 K T(J,K,Q): T = K(t)Q(t) + J(t)Q’(t) Q Q’ J K T Example: Implement a JK flip-flip using a T flip-flop 13

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