Sequential circuits Analysis Design March 16, 2020 Patrice - PowerPoint PPT Presentation

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 flip- flop 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 • Example: design a sequential system with two bits of state and two external inputs, 𝑔𝑥 and 𝑐𝑥 , with the following behaviour: – do nothing when 𝑔𝑥 = 0 and 𝑐𝑥 = 0 – Reset state to 0 when 𝑔𝑥 = 1 and 𝑐𝑥 = 1 – Advance forward through the sequence … , 2,1,3,0,2,1, … when 𝑔𝑥 = 1 and 𝑐𝑥 = 0 – Advance backward through the sequence … , 2,1,3,0,2,1, … when 𝑔𝑥 = 0 and 𝑐𝑥 = 1 • In other words, advance through the sequence … 0,3,1,2,0,3, … – A sequence generator with reset March 16, 2020 Patrice Belleville / Geoffrey Tien 6

Sequential circuit design Sequence generator with reset • Approach 1: individual bits of state implemented using D flip- flops – 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 + + 𝑹 𝟐 𝑹 𝟏 𝒈𝒙 𝒄𝒙 𝑹 𝟐 𝑹 𝟏 𝒆 𝟐 𝒆 𝟏 0 0 0 0 Sequence: 2, 1, 3, 0… 0 0 0 1 𝑔𝑥 ∙ 𝑐𝑥 = 00 : no chg 0 0 1 0 𝑔𝑥 ∙ 𝑐𝑥 = 11 : reset 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 The 𝑒 columns will be the 1 0 0 1 same as the 𝑅 + columns 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 March 16, 2020 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 • Approach 3: Load a register with constant values selected by a multiplexer – Arrange the multiplexer’s select bits in the same order as the state/input columns in the truth table – Supply constant values to multiplexer’s data inputs according to 𝑒 inputs of each row 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