Feedback and Flip-Flops Philipp Koehn 7 September 2019 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 The Story So Far 1 • We can encode numbers • We can do calculation • ... but it's all a bit static • How about a counter? ! this requires "memory" Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 2 feedback Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 A Strange Contraption 3 - + Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Let's Turn It On 4 - + Electricity is on ! this opens the normally closed key Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Let's Turn It On 5 - + Electricity is off ! this closes the normally closed key Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Do We Have? 6 • A Buzzer • A Clock • An Oscillator NOT (symbol) Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Oscillator 7 • Period of oscillator • Frequency: cycles per second • Unit: 1 cycle per second: 1 Hertz • Modern computes: Billions of Hertz = Gigahertz (GHz) Heinrich Hertz 1857--1894 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 8 flip flop Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Another Contraption 9 NOR V NOR OUT V Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Closing Upper Key 10 NOR V NOR OUT V Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Opening Upper Key 11 NOR V NOR OUT V Same key configuration as initially But: Now OUT is on --- we remembered the key turn Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Closing Lower Key 12 NOR V NOR OUT V Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Opening Lower Key 13 NOR V NOR OUT V Back to initial state Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Memory 14 • We have memory -- called Reset-Set Flip-Flop • Truth table UPPER LOWER OUT 0 0 OUT 0 1 0 1 0 1 1 1 Illegal • UPPER = SET • LOWER = RESET Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Re-Arranged 15 S NOR NOR Q R Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Symmetric 16 S NOR Q NOR Q R Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Truth Table 17 S R Q Q¯ 1 0 1 0 0 1 0 1 0 0 Q Q¯ 1 1 Illegal Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 18 d-type flip flop Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Vision 19 • Control bit ("clock") { on = write to memory { off = read from memory • Data bit { data item to be written • Output { current state of the memory Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Replace Set/Reset with Data 20 DATA NOR Q NOT NOR Q Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Add Control Bit ("Clock") 21 DATA AND NOR Q NOT CLOCK NOR Q AND Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 D-Type Flip-Flop 22 • Also called D-type latch • Circuit latches on one bit of memory and keeps it around • Truth table Data Clock Q Q¯ 0 1 0 1 1 1 1 0 X 0 Q Q¯ • Can also build these for multiple data bits Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 23 accumulative adder Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Design Goal 24 • Adder has initially value 0 • Adding a number ! value increases • Resetting ! value goes back to 0 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Ingredients 25 A7 A6 A5 A4 A3 A2 A1 A0 B7 B6 B5 B4 B3 B2 B1 B0 CO 8-BIT ADDER CI S7 S6 S5 S4 S3 S2 S1 S0 D7 D6 D5 D4 D3 D2 D1 D0 CLK 8-BIT LATCH Q7 Q6 Q5 Q4 Q3 Q2 Q1 Q0 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Ingredients 26 8 8 A B CO 8-BIT ADDER CI S 8 8 D CLK 8-BIT LATCH Q 8 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 27 0 8 • Latch: current sum CLOCK CLK D 8-BIT LATCH Q • Clock on ! set it to 0 8 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 28 0 8 • Adder CLOCK CLK D 8-BIT LATCH Q IN • Combines 8 8 { current value A B 8-BIT ADDER { selected input CO S CI 8 OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 29 0 8 • Can we pass output CLOCK CLK D 8-BIT LATCH directly to latch? Q IN 8 8 Concerns • A B 8-BIT ADDER { select between 0 and sum CO S CI { only stored when clock on 8 OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 30 0 8 8 Clear A B 2-1 SELECTOR S 8 • 2-1 selector CLOCK CLK D 8-BIT LATCH Q IN • Either uses 0 or sum 8 8 A B • Built with AND gates 8-BIT ADDER CO S CI 8 • Still have runaway feedback loop... OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 31 0 8 8 Clear A B • Two Latches 2-1 SELECTOR S { one to store the sum 8 CLOCK1 CLK D { one to store input to adder 8-BIT LATCH QS • Clock 1 8 CLOCK2 CLK D 8-BIT LATCH { carry out addition Q IN { store result 8 8 A B • Clock 2 8-BIT ADDER CO S CI { transfer to set up next addition 8 OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Building an Accumulative Adder 32 0 8 8 Clear A B • Combine the clocks 2-1 SELECTOR S Add 8 • Pressing the add key CLK D 8-BIT LATCH NOT { carry out addition QS { store result in upper latch 8 CLK D 8-BIT LATCH IN • Release the add key Q 8 8 { transfer to lower latch A B { set up next addition 8-BIT ADDER CO S CI 8 OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Else? 33 0 8 8 Clear A B 2-1 SELECTOR S • Remember the oscillator? Add 8 CLK D 8-BIT LATCH NOT QS 8 CLK D 8-BIT LATCH Q IN 8 8 NOT A B 8-BIT ADDER CO S CI 8 OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Else? 34 0 8 8 Clear A B 2-1 SELECTOR S 8 NOT CLK D 8-BIT LATCH NOT QS 8 CLK D 8-BIT LATCH Q IN • Each cycle of oscillator: 8 8 A B keeps adding 8-BIT ADDER CO S CI 8 OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 What Else? 35 0 8 8 Clear A B 2-1 SELECTOR S 8 NOT CLK D 8-BIT LATCH NOT QS 8 CLK D 8-BIT LATCH Q IN • We have something interesting here 8 8 A B 8-BIT ADDER CO S CI 8 OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 36 edge triggered flip-flop Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 D-Type Latch 37 D Q LATCH CLK Q • When clock is on, save data • "Level-triggered" Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 D-Type Latch 38 D Q D Q LATCH LATCH NOT CLK Q CLK Q • "Edge-triggered": changes value, when switched from 0 to 1 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Edge Triggered D-Type Latch 39 D Q > CLK Q Symbol Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Truth Table 40 Data Clock Q Q¯ 0 " 0 1 1 " 1 0 X 0 Q Q¯ Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 41 ripple counter Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Oscillator and Latch 42 D Q NOT > CLK Q Data Clock Q Q¯ 1 0 0 1 1 " 1 0 0 1 1 0 0 0 1 0 0 " 0 1 1 1 0 1 1 0 0 1 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Oscillator and Latch 43 D Q NOT > CLK Q Data Clock Q Q¯ 1 0 0 1 1 " 1 0 0 1 1 0 0 0 1 0 0 " 0 1 1 1 0 1 1 0 0 1 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Halving of Frequency 44 Data Clock Q Q¯ 1 0 0 1 1 " 1 0 0 1 1 0 0 0 1 0 0 " 0 1 1 1 0 1 1 0 0 1 IN OUT Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Multiple Bits 45 OUT0 OUT1 OUT2 OUT3 NOT D Q D Q D Q NOT > CLK Q > CLK Q > CLK Q OUT0 OUT1 OUT2 OUT3 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019 Ripple Counter 46 OUT0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 OUT1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 OUT2 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 OUT3 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Philipp Koehn Computer Systems Fundamental: Feedback and Flip-Flops 7 September 2019.