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String Recognizer Example
Recognize the string: 1011 Input: Output: State Machine:
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String Recognizer Example (cont.)
State Table:
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String Recognizer Example (cont.)
Implementation:
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FSMs & Flip Flops Sometimes may be more efficient to implement FSM with other Flip Flops that Dff Approach: Given state table & Flip Flop Excitation table, determine how to use Flip Flop for this circuit J-K Excitation Table:
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Parity with J-K (cont.) Implementation:
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Parity with T T Excitation Table:
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Vending Machine with J-K
J-K Excitation Table:
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FSM Word Problem: Traffic Light Controller
A busy highway is intersected by a little used farmroad. Detectors C sense the presence of cars waiting on the farmroad. With no car on farmroad, light remain green in highway direction. If vehicle on farmroad, highway lights go from Green to Yellow to Red, allowing the farmroad lights to become green. These stay green only as long as a farmroad car is detected but never longer than a set interval. When these are met, farm lights transition from Green to Yellow to Red, allowing highway to return to green. Even if farmroad vehicles are waiting, highway gets at least a set interval as green. Assume you have an interval timer that generates a short time pulse (TS) and a long time pulse (TL) in response to a set (ST) signal. TS is to be used for timing yellow lights and TL for green lights.
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Traffic Light Controller (cont.)
Picture of Highway/Farmroad Intersection:
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Traffic Light Controller (cont.)
• Tabulation of Inputs and Outputs: Input Signal reset C TS TL Output Signal HG, HY, HR FG, FY, FR ST Description place FSM in initial state detect vehicle on farmroad short time interval expired long time interval expired assert green/yellow/red highway lights assert green/yellow/red farmroad lights start timing a short or long interval • Tabulation of Unique States: Some light configuration imply others State S0 S1 S2 S3 Description Highway green (farmroad red) Highway yellow (farmroad red) Farmroad green (highway red) Farmroad yellow (highway red)
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Traffic Light Controller (cont.)
State Diagram
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Traffic Light Controller (cont.)
State Table using J-K Flip Flops
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Registers Storage unit. Can hold an n-bit value
Composed of a group of n flip-flops Each flip-flop stores 1 bit of information Normally use D flip-flops D Q Dff clk D Q Dff clk D Q Dff clk D Q Dff clk
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Controlled Register D Q Dff clk D Q Dff clk D Q Dff clk D Q Dff clk
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Shift Register Register that shifts the binary values in one or both directions D Q Dff clk In Out Clock
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Transfer of Data 2 modes of communication: Parallel vs. Serial
Parallel: all bits transferred at the same time Serial: one bit transferred at a time Shift register can be used for serial transfer D Q Dff clk
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Shift Register w/Parallel Load
D Q Dff clk D Q Dff clk D Q Dff clk D Q Dff clk
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Bidirectional Shift Register w/Parallel Load
D Q Dff clk D Q Dff clk D Q Dff clk D Q Dff clk
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Conversion between Parallel & Serial
LSI LSI D Q3 4-bit D Q2 Shift D Q1 Reg. D Q0 Shift Load Clk D Q3 4-bit D Q2 Shift D Q1 Reg. D Q0 Shift Load Clk
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Counters A reg. that goes through a specific state sequence
n-bit Binary Counter: counts from 0 to 2N-1 in binary Up Counter: Binary value increases by 1 Down Counter: Binary value decreases by 1 3-bit binary up counter state diagram:
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Binary Up-Counter Imp. (D Flip-Flop)
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Binary Up-Counter Imp. (T Flip-Flop)
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Complex Binary Counter
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Arbitrary Sequence Counters
Design a 3-bit count that goes through the sequence 000->010->100->101->111->110->001->011->000->...
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Memory Need method for storing large amounts of data
Computer programs, data, pictures, etc. RAM: Random Access Memory, Read/Write ROM: Read-only Memory 64x8 RAM A D7 A D6 A D5 A D4 D3 D2 D1 Write D0
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8x4 RAM In3 In2 In1 In0 Write A2 A1 A0 Out3 Out2 Out1 Out0 000 001 010
011 100 101 110 111 3:8 Decoder Enable S2 S1 S0 A2 A1 A0 Out Out Out Out0
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RAM Cell Requirements: Store one bit of data
Change data based on input when row is selected Input S Q R Row Select
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RAM Expansion Implement a big RAM from multiple small RAMS
Address D15 D14 D13 D12 D11 D10 D9 D8 D7 D6 D5 D4 D3 D2 D1 D0
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RAM Expansion (cont) Build a 16x16 RAM from 16x4 RAMs 16x4 RAM A3 Din
A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write
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RAM Expansion (cont) Build a 32x16 RAM from 16x4 RAMs 16x4 RAM A3 Din
A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write 16x4 RAM A Din A2 A Dout A0 Write
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