Patterns in Numbers

THE MAGAZINE FOR COMPUTER APPLICATIONS
Circuit Cellar Online offers articles illustrating creative solutions
and unique applications through complete projects, practical
tutorials, and useful design techniques.

PATTERNS IN NUMBERS

Technically Speaking A State Machine Design for Binary Pattern Recognition

by James Antonakos

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

STATE TRANSITION TABLE

The state transition information is shown in Table 2. The present state column (ABi) is the state of the machine before a clock pulse. The present state is a combination of the state number outputs (A for Q_A, B for Q_B,) and the current input bit (i).

Present state ABi	Next state AB	Ja, Ka	Jb, Kb
000	00	0, x	0, x
001	01	0, x	1, x
010	10	1, x	x, 1
011	11	1, x	x, 0
100	00	x, 1	0, x
101	01	x, 1	1, x
110	10	x, 0	x, 1
111	11	x, 0	x, 0
Table 2ıHere you can see the state transition table for the divide by four detector. The J/K values shown are required to excite the state number flip-flops into the correct state sequence depending on the input, i.

The next state column (AB) indicates the new state of the machine after a clock pulse has occurred. To fill in the Ja, Ka and Jb, Kb columns, compare the A-to-A and B-to-B bit transitions (0-0, 0-1, 1-0, 1-1) in the present state and next state columns, and enter the appropriate J/K excitation values.

PREVIOUS • NEXT

Circuit Cellar provides up-to-date information for engineers. Visit www.circuitcellar.com for more information and additional articles.
For subscription information, call (860) 875-2199, subscribe@circuitcellar.com or subscribe online. ıCircuit Cellar, the Magazine for Computer Applications. Posted with permission.