State graph of 2 stage lift

[jonnybgood]

Hi,
attached is the stage graph of a two stage lift. Is it a good idea to use a one flip flop per state to derive the input equations using D-type flip flops? Also, in the next state should I include the inverted signals as well?

 

[ArNvC]

This type of implementation (FSM) involves Flip Flops. The selection of the Flip Flop to use is arbitrary and usually is determined by cost factors. The best choice is to perform both analysis and decide which type of Flip Flop results in minimum number of logic gates and lesser cost.
Yes, take into account past inputs in order to decide on the output.

 

[jonnybgood]

In the exercise I was asked to use D type FF. Attached is the state table. Did I implemented it correctly? I i am not mistaken now I just need to derive the next state equations for input of the six FFs. Each equation will contain 8 products summed together.

 

[ArNvC]

yes, looks good to me.

 

[jonnybgood]

Attached are the derived d-type FF input equations.

One last question if I had to derive the equations using the karnaugh map approach, would I have to include next states for all combination of the 5 inputs? that is I will have 2^5 = 32 next state columns? (DC, N1, N2, Fs1, Fs2) or shall I work only with the same columns used for the previous one hot state table? And when filling up the karnaugh maps, the undefined will give them 0's or don't cares??

thanks

 

[ArNvC]

Hi,
For understanding, lets take a 3 state FSM.
For every Flip Flop add one more column in the State table with the name of the Flip Flop's input, "D" for this case. The column that corresponds to each Flip Flop describes what input we must give the Flip Flop in order to go from the Current State to the Next State. For the D - Flip Flop this is easy: The necessary input is equal to the Next State. In the rows that contain X's we fill X's in this column as well.

 

[jonnybgood]

thanks for the explanation but I think I was not clear enough in my question. When I asked about the columns I was referring to the number Next State columns, that depends on the number of inputs (in my case 5). In the image you showed me it is quite a simple one since there is only one input. My confusion is whether I should fill in 2^5 = 32 next state columns or whether the columns DC, DC', N1N2', N1'N2, Fs1, Fs1', Fs2, Fs2' are enough?? (I am not considering one-hot approach here, I will only have 3 FF for 6 states which are enough).

 

[ArNvC]

The Next State Columns are as many as the Current State columns.
For next state, fill it in with the state that it reaches when, in the State Diagram, from the Current State of the same row following the Input of the same row. If you get to a row whose Current State number doesn't correspond to any actual State in the State Diagram then fill it with Don't Care terms (X).