Sequential circuits Analysis Design March 16 2020 Patrice

Sequential circuits Analysis Design March 16, 2020 Patrice Belleville / Geoffrey Tien 1

Announcements • Classes moved online due to COVID-19 precautions • Midterm 2 will take place ONLINE tomorrow at the scheduled time – Instructions for access, guidelines, and submission will be announced on Piazza • Please pause the recorded video if you need to write anything or we have an exercise • Please bear with the poor lighting and recording quality – this will hopefully improve after I purchase some new equipment March 16, 2020 Patrice Belleville / Geoffrey Tien 2

Exercise Sequential circuit analysis • Determine the behaviour of the following sequential system: March 16, 2020 Patrice Belleville / Geoffrey Tien 3

Sequential circuits Design March 16, 2020 Patrice Belleville / Geoffrey Tien 4

Sequential circuit design • All of the same techniques of design and analysis from combinational circuits also apply to sequential design – Karnaugh maps, recognizers, etc. – Now, the system state (flip-flop outputs) are included as "inputs" • We start with a specification of the states, transitions, inputs, and sequential devices to be used in the construction – based on the understood behaviour of the sequential device (e. g. D flipflop or register), and the required transition, determine the inputs necessary to cause the required transition to occur March 16, 2020 Patrice Belleville / Geoffrey Tien 5

Sequential circuit design • March 16, 2020 Patrice Belleville / Geoffrey Tien 6

Sequential circuit design Sequence generator with reset • Approach 1: individual bits of state implemented using D flipflops – Construct a truth table • current state and external inputs as "input" • next state as "output" • determine propositional logic statements/functions to produce the necessary transition from each current state to the next state. March 16, 2020 Patrice Belleville / Geoffrey Tien 7

Sequential circuit design Sequence generator with reset – approach 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 March 16, 2020 1 1 Patrice Belleville / Geoffrey Tien 8

Sequential circuit design Sequence generator with reset – approach 1 All signals are 1 bit wide March 16, 2020 Patrice Belleville / Geoffrey Tien 9

Sequential circuit design Sequence generator with reset – approach 2 • Approach 2: Load a register with values from a semantic analysis – Not applicable to this problem • Study the required behaviours, and use combinational components (possibly with feedback loops) to achieve individual functions – E. g. use full adders for addition/increment, use subtractors for subtraction/decrement, etc. • Select between the individual functions using multiplexer(s) March 16, 2020 Patrice Belleville / Geoffrey Tien 10

Sequential circuit design Sequence generator with reset – approach 3 • March 16, 2020 Patrice Belleville / Geoffrey Tien 11

Sequential circuit design Sequence generator with reset – approach 3 Data signals are 2 bits wide March 16, 2020 Patrice Belleville / Geoffrey Tien 12

Sequential circuit design Practice • How to make random practice problems – Decide how many state/input bits you want – From a DFA-like state transition diagram, randomly draw some transitions to various states on specified inputs – Create a truth table from your state transition diagram • There may be some unspecified rows – this is generally OK just for practice and become “don’t-care” rows in your design – see Geoff’s optional Karnaugh map slides from January (between slide sets 05 and 06) March 16, 2020 Patrice Belleville / Geoffrey Tien 13