Algorithm = Logic + Control Sequential Circuits Problems(I) Chapter 2 Prof. Sin-Min Lee Department of Mathematics and Computer Science
We wish to design a synchronous sequential circuit whose state diagram is shown in Figure. The type of flip-flop to be use is J-K Two flip-flops are needed to represent the four states and are designated Q0Q1. The input variable is labelled x.
. Excitation table for JK flip-flop Excitation table of the circuit
The simplified Boolean functions for the combinational circuit can now be derived
How do we determine the combinatorial ciccuit? • This circuit has three inputs, I, R, and the current A. • It has one output, DA, which is the desired next A. • So we draw a truth table, as before. • For convenience I added the label Next A to the DA column • But this table is simply the truth table for the combinatorial circuit.
A divide-by-three counter which outputs one 1 for every 3 1's seen as input (not necessarily in succession.) After outputting a 1, it starts counting all over again. 1. To build this, will need three states, corresponding to 0, 1, or 2 1's seen so far.
Designing with JK Flip-Flops • The design of a sequential circuit with other than the D type is complicated by the fact that the flip-flop input equations for the circuit must be derived indirectly from the state table. When D-type flip-flops are employed, the input equations are obtained directly from the next state. This is not the case for JK and other types of flip-flops. In order to determine the input equations for these flip-flops, it is necessary to derive a functional relationship between the state table and the input equations.
Flip-Flop Excitation Tables • A table that lists the required inputs for a given change of state is known as an excitation table. Example of an excitation table is shown below:
Flip-Flop Excitation Tables (cont) The excitation table show four different types of flip-flops. Each table has a column for the present state Q(t), a column for the next state Q(t + 1), and a column for each flip-flop input to show how the required transition is achieved. The symbol X in the table represents a don’t-care condition, which means that it does not matter whether the input is 0 or 1.
Flip-Flop Excitation Tables (cont) The excitation table for the D flip-flop shows that the next state is always equal to the D input and is independent of the present state. This can be represented algebraically: D = Q(t + 1)
Design Procedure • The design procedure for sequential circuits with JK flip-flops is the same as that for sequential circuits with D flip-flops, except that the input equations must be evaluated from the present-state to next-state transition derived from the excitation table.
Design Procedure (cont) • The advantage of using JK-type flip-flops when designing sequential circuits is that there are so many don’t-care entries indicates that the combinational circuit for the input equations is likely to be simpler, because don’t-care minterms usually help in obtaining simpler expressions.
Design Procedure (cont) In order to perform the simulation, a clock, as well as the input signals R and X, is required. In doing the simulation of any sequential circuit, sufficient time must be provided in the clock period for each of the following: 1. All flip-flops and inputs to change; 2. The effects of these changes to propagate through the combinational logic of the circuit to the flip-flop inputs; and 3. The setup of the flip-flops for the next clock edge to occur.