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PATTERNS IN NUMBERS

A State Machine Design for Binary Pattern Recognition

by James Antonakos

Start ý The Problem ý Enumeration ý State Diagram Approach ý A Little Synchronous Logic ý State Transition Table ý Let Karnaugh Maps Find the Patterns ý A Hotshot One-Shot ý The Real Thing ý Other Implementations ý I Challenge Youý ý Sources and PDF

A LITTLE SYNCHRONOUS LOGIC

Synchronous logic can be used to implement the state diagram. Because there are four states, you use just two bits to keep track of the state number. Thus, 00 is for state zero, 01 is for state one, 10 is for state two, and 11 is for state three. A pair of J/K flip-flops should be used to maintain the state number, and youýll need a combinational logic circuit to control the J/K flip-flops.

Table 1 shows the required J/K excitation values needed to get the J/K flip-flop to change states properly. For example, to get the Q output to go from a one before the clock pulse to a zero after the clock pulse, the J and K inputs must be set to J = x (0 or 1) and K = 1 to obtain the transition. Table 1 is used to help fill in the state transition table.

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