Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No. 20-1 Chapter #7: Sequential Logic Case Studies 7.4 Counters.

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Presentation transcript:

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Chapter #7: Sequential Logic Case Studies 7.4 Counters

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different Kinds of FFs R-S Flipflops Continuing with the 000, 010, 011, 101, 110, 000,... counter example RS Exitation Table Remapped Next State Functions Present State Next State Remapped Next State Q+ = S + R Q Q Q + R S 0 0 X X C B A C + B + A + RC SC RB SB RA SA X X X X X X X X X X X X 0 0 X X X X X X X X X X X X X X X X X X X X X X

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different Kinds of FFs RS FFs Continued CB A 0 1 RC CB A 0 1 RA CB A 0 1 RB CB A 0 1 SC CB A 0 1 SA CB A 0 1 SB RC = A SC = A RB = A B + B C SB = B RA = C SA = B C X X 1 X X X X 1 X X X X 1 X 0 1 X 0 X X 0 X 1 X 0 X X X 0 X X X X X 0 3 gates 11 input literals + FF connections

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation With Different Kinds of FFs RS FFs Continued Resulting Logic Level Implementation: 3 Gates, 11 Input Literals + Flipflop connections

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different FF Types J-K FFs J-K Excitation Table Remapped Next State Functions Present State Next State Remapped Next State Q+ = J Q + K Q Q Q + J K X X 1 0 X X 0 C B A C+ B+ C+ JC KC JB KB JA KA X 1 X 0 X X X X X X X X X X X X 0 1 X X X 1 X X X X X X X X X X X 0 1 X X X 1 X 1 0 X X X X X X X X X X

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different FF Types J-K FFs Continued CB A 0 1 JC CB A 0 1 JA CB A 0 1 JB CB A 0 1 KC CB A 0 1 KA CB A 0 1 KB JC = A KC = A JB = 1 KB = A + C JA = B C KA = C 0 0 X X X 1 X X X X 1 X X X X 0 1 X X X X X X 1 X 0 1 X X 1 X X X X X X 0 X 1

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different FF Types J-K FFs Continued Resulting Logic Level Implementation: 2 Gates, 10 Input Literals + Flipflop Connections

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different FF Types D FFs Simplest Design Procedure: No remapping needed! C + = DC = A B + = DB = A C + B A + = DA = B C Resulting Logic Level Implementation: 3 Gates, 8 Input Literals + Flipflop connections

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different FF Types Comparison T Flip-flops:5 gates,10 literals15 wires R-S Flip-flops:3 gates,5 literals12 wires J-K Flip-flops:2 gates,4 literals9 wires D Flip-flops:3 gates,5 literals9 wires

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No Implementation with Different FF Types Comparison T FFs well suited for straightforward binary counters But yielded worst gate and literal count for this example! No reason to choose R-S over J-K FFs: it is a proper subset of J-K R-S FFs don't really exist anyway J-K FFs yielded lowest gate count Tend to yield best choice for packaged logic where gate count is key D FFs yield simplest design procedure Best literal count D storage devices very transistor efficient in VLSI Best choice where area/literal count is the key

Contemporary Logic Design Sequential Case Studies © R.H. Katz Transparency No HW #18 -- Sections 7.1, 7.2, 7.4