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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

LET KARNAUGH MAPS FIND THE PATTERNS

To build the simplest digital machine, you need to design the circuitry to drive the J/K inputs of each flip-flip from a set of minimized logic equations. Because there are only three bits (A, B, and i) to work with, a three-input Karnaugh map can be easily used to solve for the minimal logic equation. Figure 2 shows the four Karnaugh maps associated with the J/K input signals, including the associated solutions. Note that the "donýt care" x values help minimize the results in each map.

Figure 2aýdýExcitation values from the state transition table are entered into Karnaugh maps and solved. The equations from each map are Ja = B, Ka = *B, Jb = I, and Kb = *i.

Figure 3 shows a schematic of the digital machine with simplified 0/1 input logic to allow you to enter the serial pattern using two push buttons (a zero button and one button). The NOR gate on the Q_A and Q_B outputs detects when the outputs are both low and illuminates the LED to indicate that the input number is evenly divisible by four. All you need to do is generate an input bit and clock pulse for each press of the zero or one buttons.

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