CpE358/CS381. Switching Theory and Logical Design. Class 10

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1 CpE358/CS38 Switching Theory and Logical Design Class CpE358/CS38 Summer- 24 Copyright

2 Today Fundamental concepts of digital systems (Mano Chapter ) Binary codes, number systems, and arithmetic (Ch ) Boolean algebra (Ch 2) Simplification of switching equations (Ch 3) Digital device characteristics (e.g., TTL, CMOS)/design considerations (Ch ) Combinatoric logical design including LSI implementation (Chapter 4) Flip-flops and state memory elements (Ch 5) Sequential logic analysis and design (Ch 5) Counters, shift register circuits (Ch 6) Hazards, Races, and time related issues in digital design (Ch 9) Synchronous vs. asynchronous design (Ch 9) Memory and Programmable logic (Ch 7) Minimization of sequential systems Introduction to Finite Automata CpE358/CS38 Summer- 24 Copyright

3 Course Roadmap Logic Circuits with gates CpE358/CS38 Summer- 24 Copyright

4 Course Roadmap Combinatorial Circuits Logic Circuits with gates CpE358/CS38 Summer- 24 Copyright

5 Course Roadmap Combinatorial Circuits Logic Circuits with gates Logic Circuits with memory CpE358/CS38 Summer- 24 Copyright

6 Course Roadmap Combinatorial Circuits Logic Circuits with gates Sequential Circuits Logic Circuits with memory CpE358/CS38 Summer- 24 Copyright

7 Course Roadmap Combinatorial Circuits Logic Circuits with gates Sequential Circuits Logic Circuits with memory Specific Specific functions CpE358/CS38 Summer- 24 Copyright

8 Course Roadmap Combinatorial Circuits Logic Circuits with gates Sequential Circuits Logic Circuits with memory Specific Specific functions Registers and Counters CpE358/CS38 Summer- 24 Copyright 24-38

9 Shift Register S I D D D D D D D S O Clk Present Input Next Output S I S I S = 6 N-bit S/R S I S O SISO Register Serial-in, Serial-out CpE358/CS38 Summer- 24 Copyright 24-38

10 Shift Register Variants S I D D D D D D D S O Clk 2 N- SIPO Register S I N-bit S/R S O Serial-in, Parallel-out CpE358/CS38 Summer- 24 Copyright

11 Shift Register Variants D D D 2 2 D 3 3 D 4 4 D 5 5 D 6 6 D D D D D D D Clk D D D 2 D N- N-bit S/R PIPO Register Parallel-in, Parallel-out 2 N- CpE358/CS38 Summer- 24 Copyright

12 Shift Register Variants D N-2 D N- N- S I D D D S O Clk P/S D D D 2 D N- P/S S I N-bit S/R S O Serial/Parallel Register Parallel-in/Serial-in, Parallel-out/Serial-out 2 N- CpE358/CS38 Summer- 24 Copyright

13 Tandem S/Rs Serial registers 2N-bit S/R S I N-bit S/R S O S I N-bit S/R S O CpE358/CS38 Summer- 24 Copyright

14 Generic Moore Machine j Outputs m n B/ Transition Controls A/ C/ Inputs k All state-to-state transitions are potentially allowable. CpE358/CS38 Summer- 24 Copyright

15 S/R-based Moore Machine S/R j Outputs n B/ Transition Controls A/ C/ Inputs k Only specific state-to-state transitions are allowable. CpE358/CS38 Summer- 24 Copyright

16 Shift Register Sequences Transition Controls Output Mapping S I I N-bit S/R S O CpE358/CS38 Summer- 24 Copyright

17 Shift Register Sequences Input Transition Controls Output Mapping S I I N-bit S/R S O S I = ABCDE S I = BCDE BCDE S I = S I = S I = S I = BCD BCD BCD BCD CpE358/CS38 Summer- 24 Copyright

18 S/R Data Scrambler/Encryptor Fracasi scrambler: S/R Sequential Function F(x) S/R Sequential Function F(x) Input Data + + Descrambled Data CpE358/CS38 Summer- 24 Copyright 24-39

19 S/R Data Scrambler/Encryptor Fraccassi scrambler: N-bit S/R N-bit S/R N-bit S/R N-bit S/R N-bit S/R N-bit S/R Input Data + + Descrambled Data CpE358/CS38 Summer- 24 Copyright 24-39

20 Course Roadmap Combinatorial Circuits Logic Circuits with gates Sequential Circuits Logic Circuits with memory Specific Specific functions Registers and Counters CpE358/CS38 Summer- 24 Copyright

21 Generic Moore Machine j Outputs m n B/ Transition Controls A/ C/ Inputs k All state-to-state transitions are potentially allowable. CpE358/CS38 Summer- 24 Copyright

22 Counter Moore Machine Counter j Outputs m n B/ Transition Controls A/ C/ Inputs k -to-state transitions follow a counting sequence Inputs (if any) may be used to set counting range, direction, starting point CpE358/CS38 Summer- 24 Copyright

23 Counters Binary Ripple Counter J A K A CpE358/CS38 Summer- 24 Copyright

24 Counters Binary Ripple Counter J A J B K K A B CpE358/CS38 Summer- 24 Copyright

25 Counters Binary Ripple Counter J A B C J J K K K A B C CpE358/CS38 Summer- 24 Copyright

26 Binary Ripple Counter (idealized) Counters J A B C J J K K K A B C CpE358/CS38 Summer- 24 Copyright

27 Binary Ripple Counter (more realistic) Counters J A B C J J K K K A B C { { { { { { { CpE358/CS38 Summer- 24 Copyright

28 Cascading Counters T CpE358/CS38 Summer- 24 Copyright 24-4

29 Cascading Counters T T CpE358/CS38 Summer- 24 Copyright 24-4

30 Cascading Counters T T T CpE358/CS38 Summer- 24 Copyright 24-42

31 Cascading Counters T T T T N CpE358/CS38 Summer- 24 Copyright 24-43

32 Cascading Counters T T T T N CpE358/CS38 Summer- 24 Copyright 24-44

33 Ripple Counters vs. Synchronous Counters F JAR (A,B,C) J A B C F JBR (A,B,C) J F JBR (A,B,C) J F KAR (A,B,C) K F KBR (A,B,C) K F KBR (A,B,C) K F JAS (A,B,C) J A B C F JBS (A,B,C) J F JBS (A,B,C) J F KAS (A,B,C) K F KBS (A,B,C) K F KBS (A,B,C) K CpE358/CS38 Summer- 24 Copyright 24-45

34 Synchronous Counters BCD Counter: table Present Next CpE358/CS38 Summer- 24 Copyright 24-46

35 Synchronous Counters BCD Counter: J-K inputs BA DC BA DC J A K A J B K B Present Next J C J D K C K D J-K operation: CpE358/CS38 Summer- 24 Copyright 24-47

36 J A J B J C J D BCD Counter: J-K inputs BA DC CpE358/CS38 Summer- 24 Synchronous Counters BA DC K A K B K C K D Copyright 24 J-K operation: Present Next -48

37 J A J B J C J D BCD Counter: J-K inputs BA DC CpE358/CS38 Summer- 24 Synchronous Counters BA DC K A K B K C K D Copyright 24 J-K operation: Present Next -49

38 J A J B J C J D BCD Counter: J-K inputs BA DC CpE358/CS38 Summer- 24 Synchronous Counters BA DC K A K B K C K D Copyright 24 J-K operation: Present Next -4

39 J A J B J C J D BCD Counter: J-K inputs BA DC CpE358/CS38 Summer- 24 Synchronous Counters BA DC K A Copyright 24 K B J A = K A = J B = AD K C K B = A K D J C = AB K C = AB J D = ABC K D = A Present Next -4

40 Synchronous Counters BCD Counter J A B C J J J D K K K K J A = K A = J B = AD K B = A J C = AB K C = AB J D = ABC K D = A Present J D K D J C K C J B K B J A K A Next Present J D K D J C K C J B K B J A K A Next CpE358/CS38 Summer- 24 Copyright 24-42

41 Synchronous Counters BCD Counter Present J D K D J C K C J B K B J A K A Next Present J D K D J C K C J B K B J A K A Next CpE358/CS38 Summer- 24 Copyright 24-43

42 Varieties of Counters Counters with Parallel Load Normal counter operation Load C I D 3 D 2 D D Next C O D D D 2 D 3 C I C O LD 2 3 ABCD ABCD WYZ WYZ CpE358/CS38 Summer- 24 Copyright 24-44

43 Varieties of Counters Counters with Parallel Load Normal counter operation Load C I D 3 D 2 D D Next C O D D D 2 D 3 C I C O LD 2 3 ABCD ABCD WYZ WYZ CpE358/CS38 Summer- 24 Copyright 24-45

44 Varieties of Counters Counters with Parallel Load Loading next state in parallel Load C I D 3 D 2 D D Next C O D D D 2 D 3 = ABCD C I C O LD > ABCD ABCD ABCD WYZ WYZ CpE358/CS38 Summer- 24 Copyright 24-46

45 Varieties of Counters Counters with Parallel Load Load C I D 3 D 2 D D Next C O D D D 2 D 3 C I C O LD 2 3 ABCD ABCD WYZ WYZ CpE358/CS38 Summer- 24 Copyright 24-47

46 Varieties of Counters Counters with Parallel Load Load C I D 3 D 2 D D Next C O D D D 2 D 3 C I C O LD 2 3 ABCD ABCD WYZ WYZ CpE358/CS38 Summer- 24 Copyright 24-48

47 Cascading Synchronous Counters D D D 2 D 3 D D D 2 D 3 D D D 2 D 3 C I A C O LD C I C O B C LD LD C I C O A A 2A 3A C OA B CpE358/CS38 Summer- 24 Copyright 24-49

48 Programmable Synchronous Counters LSB D D D 2 D 3 D D D 2 D 3 MSB D D D 2 D 3 C I A C O LD C I B C O LD C I C C O LD Assume D 3C D A = b b b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b b Next C OA C OB C OC b b b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b b b b b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b b + ABCD EFGH ABCD EFGH+ ABCD ABCD+ b b b 9 b 8 b 7 b 6 b 5 b 4 b 3 b 2 b b CpE358/CS38 Summer- 24 Copyright 24-42

49 Applications of Programmable Counters Programmable divide by N frequency divider: 2 K -N CI CO CI CI CO CI CO CI LD LD LD LD /N CpE358/CS38 Summer- 24 Copyright 24-42

50 Applications of Programmable Counters Reference Oscillator Voltage Divide Phase Lowpass Controlled f By K Comparator Filter R f R /K Oscillator f S Synthesized Frequency Phase Locked Loop f S /N Divide By N Channel Selection, N f S = N K f R PLL frequency synthesizers used in TV, radio, cellular phones, PCs, modems, etc. CpE358/CS38 Summer- 24 Copyright

51 Applications of Programmable Counters Master f m Divide by f m /A A Divide by B f m /B Complex Digital System (e.g., PC) Divide by C f m /C CpE358/CS38 Summer- 24 Copyright

52 Timing Signal Generation Master f m Phase A Phase B Complex Digital System (e.g., PC) Phase C CpE358/CS38 Summer- 24 Copyright

53 Only FF is set at any given time Ring Counters s D D D D D A B C D E A B C D E CpE358/CS38 Summer- 24 Copyright

54 Switch-tail Ring Counters (Johnson Counter) A B C D D D D D A B C D E s D E CpE358/CS38 Summer- 24 Copyright

55 Summary Fundamental concepts of digital systems (Mano Chapter ) Binary codes, number systems, and arithmetic (Ch ) Boolean algebra (Ch 2) Simplification of switching equations (Ch 3) Digital device characteristics (e.g., TTL, CMOS)/design considerations (Ch ) Combinatoric logical design including LSI implementation (Chapter 4) Flip-flops and state memory elements (Ch 5) Sequential logic analysis and design (Ch 5) Counters, shift register circuits (Ch 6) Hazards, Races, and time related issues in digital design (Ch 9) Synchronous vs. asynchronous design (Ch 9) Memory and Programmable logic (Ch 7) Minimization of sequential systems Introduction to Finite Automata CpE358/CS38 Summer- 24 Copyright

56 Homework due in Class 2 Show all work Problems 6-, 6-23, 6-29 CpE358/CS38 Summer- 24 Copyright

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