6_Incompletely_Specified_Slides

# 6_Incompletely_Specified_Slides - ECE ECE 3504 Digital...

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ECE 3504 Digital Design 1 Section 6: Incompletely-Specified Synchronous Sequential Circuits

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Designing Incompletely Designing Incompletely- Specified State Machines I. Specification: Same as for completely- specified II. Circuit Modeling: Same as for completely- specified III. State Minimization a. Implication table for compatibility b. Maximal compatible sets c. Minimal covers d. Closure IV State Assignment Almost the sam IV. State Assignment – Almost the same a. Use a dense state assignment or a one- hot code state assignment. b Try to place don't care cells next to 1s b. Try to place don t care cells next to 1s (SOP) or next to 0s (POS). V. Implementation – Same as completely- specified except include don' -care cells in specified except include don t care cells in the procedure as previously described.

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Exampl Example A clocked detector circuit has inputs x 1 and x 2 and outputs z 1 and z 2 . x 1 and x 2 are level signals that change only between clock pulses. When x 1 = 1 for two successive clock periods, then the values on x 2 during the next four clock periods represent a decimal Gray Code digit. At the time of the fourth bit, z 1 = 1 if the digit received was even. z 2 = 1 if the digit was odd. At all other times that x 1 = I, z 1 z 2 = 00. If x 1 remains 1 for the two clock periods following receipt of a digit, another digit will follow, and the process will repeat until x 1 goes to 0, which only occurs between digits.
Exampl Example Decimal Digit Gray Code msb b b msb b 1 (msb) b 2 3 4 (msb) 0 0010 1 0110 2 0111 3 0101 4 0100 5 1100 6 1101 7 1111 8 1110 9 1010

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Exampl Example F J 11/00 10/00 10 00 10/10 (0) A B C D G K L A 1-/00 1 00 10/00 10/00 10/01 (1) 11/10 (2) 10/10 (4) 11/01 (3) 10 01 9 E H M N 0-/-- 0-/-- 1-/00 10/00 10/00 10/01 (9) 10/01 (5) 11/10 (6) I O 10/10 (8) 11/01 (7)
Exampl Example PS x 1 x 2 00 01 10 11 A A / -- A / -- B / 00 B / 00 B A / -- A / -- C / 00 C / 00 C - / -- - / -- D / 00 E / 00 D - / -- - / -- F / 00 G / 00 E - / -- - / -- H / 00 I / 00 / / / J / 00 F - / -- - / -- - / -- G - / -- - / -- K / 00 L / 00 H - / -- - / -- - / -- M / 00 / - / - N / 00 O / 00 I - / -- - / -- J - / -- - / -- A / 10 - / -- K - / -- - / -- A / 10 A / 01 L - / -- - / -- A / 01 A / 10 M - / -- - / -- A / 01 - / -- N - / -- - / -- A / 01 A / 10 O - / -- - / -- A / 10 A / 01 NS / z 1 z 2

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## This note was uploaded on 01/17/2011 for the course ECE 3504 at Virginia Tech.

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6_Incompletely_Specified_Slides - ECE ECE 3504 Digital...

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