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

Implementation Format and Tool Procedure Excitation Tables Example

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

Canonical Form: Mealy and Moore Machines Mealy Machine: yi(t) = fi(X(t), S(t)) Moore Machine: yi(t) = fi(S(t)) si(t+1) = gi(X(t), S(t)) x(t) x(t) C1 C2 y(t) C1 C2 y(t) CLK CLK s(t) s(t) Mealy Machine Moore Machine

iClicker The advantage of Moore machine over Mealy machine is that for Moore machine, the circuit is smaller the circuit is faster the input is synchronized with clock the output is synchronized with clock None of the above

Sequential Network Implementation: Format and Tool Canonical Form: Mealy & Moore machines State Table  Netlist Tool: Excitation Table x(t) C1 C2 y(t) CLK s(t) Q(t+1) = h(x(t), Q(t)) y(t) = f(x(t), Q(t))

Implementation: Procedure State Table => Excitation Table Given a state table, we have NS: Q(t+1) = h(X(t),Q(t)) We want to derive D(t), T(t), (S(t) R(t)), (J(t) K(t)) as functions of (X,Q(t)). We implement D, T, (S R), (J K) as combinational logic.

Implementation: Procedure F-F State Table <=> F-F Excitation Table W PS NS NS PS W W: D F-F D(t)= eD(Q(t+1), Q(t)) T F-F T(t)= eT(Q(t+1), Q(t)) SR F-F S(t)= eS(Q(t+1), Q(t)) R(t)= eR(Q(t+1), Q(t)) JK F-F J(t)= eJ(Q(t+1), Q(t)) K(t)= eK(Q(t+1), Q(t))

Implementation: Procedure State table: y(t)= f(Q(t), x(t)), Q(t+1)= h(x(t),Q(t)) Excitation table of F-Fs: D(t)= eD(Q(t+1), Q(t)); T(t)= eT(Q(t+1), Q(t)); (S, R), or (J, K) From 1 & 2, we derive excitation table of the system D(t)= gD(Q(t), x(t))= eD(h(x(t),Q(t)),Q(t)); T(t)= gT(Q(t), x(t))= eT(h(x(t),Q(t)),Q(t)); (S, R) or (J, K). Use K-map to derive optional combinational logic implementation. T(t)= gT(Q(t), x(t)) y(t)= f(Q(t), x(t))

Excitation Table State table of JK F-F: Excitation table of JK F-F: 00 1 01 10 11 Q(t) Q(t+1) JK Excitation table of JK F-F: 0- -1 1 1- -0 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 Tables and State Tables SR SR Q(t+1) NS SR PS 0- 01 1 10 -0 PS 00 1 01 10 1 11 - 1 1 Q(t) Q(t) Q(t+1) T T Q(t+1) NS T PS 1 1 PS 1 1 1 1 Q(t) Q(t) Q(t+1)

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

iClicker Given a flip-flop, the relation of its state table and excitation table is One to one One to many Many to one Many to many None of the above

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

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

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