# Lec06 - ECE 212 Digital Circuits II Wednesday 13 February...

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1 ECE 212 Digital Circuits II Wednesday, 13 February 2008 ± HW Set 6: Problem 1 Rytis U. Problem 2 Jeff V. Problem 3 Dennis W. Today's Goals ± To learn to write flip-flop input expressions from a State Transition Diagram by inspection. ± To understand the effect of state assignment on FPGA realization.

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2 Starting Point ± Your multiplier controller has, say 17 states. ± How many flip-flops do you need to realize it? ± How many flip-flops does the Xilinx realization use? 5 17 ± Why??? Clocked Circuit Design State Transition Diagram State Assignment Flip-flop input expressions. Realization (combinational circuit). The State Assignment affects the flip-flop input expressions.
3 Example State Transition Diagram State Assignment We need 3 flip-flops: Q2 Q1 Q0. State Q2 Q1 Q0 R S1 S2 S3 S4 S5 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 "We're in state R" = ?? State Q2 Q1 Q0 R S1 S2 S3 S4 S5 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Encoded states. (In R) = (In S1) = ( !Q2 & !Q1 & Q0 ) Decode the encoding. etc.

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4 D2 Expression (1/2) State Transition Diagram, with State Assignment D2 = Q2+ When will Q2+ = 1? When we enter the 100 state or we enter the 101 state. How do we enter the 100 state? The 101 state? D2 Expression (2/2) We enter the 100 state iff We enter the 101 state iff ( ! ( !M1 & M0 ) ) ( ! ( M1 & ! M0 ) ) D2 = ( ! ( !M1 & M0 ) ) | ( ! ( M1 & ! M0 ) ) OR
5 D1 Expression D1 = (We are in the 001 state) OR ( ! ( ! M1 & ! M0 ) ) D1 = ( ! Q2 & | ( ! Q2 &

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## This note was uploaded on 04/17/2008 for the course ECE 212 taught by Professor Greco during the Spring '08 term at Lafayette.

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Lec06 - ECE 212 Digital Circuits II Wednesday 13 February...

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