1. Department of Communication Engineering, NCTU 1 Unit 2 Reviews on Logic Elements

2. Department of Communication Engineering, NCTU 2 2.1 Decoders and Encoders

3. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 3 3-to-8 line decoder The i th output is 1 if the input binary value is equal to i

4. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 4 4-to-10 line decoder

5. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 5 In general a n-to-2 n decoder can generate the all 2 n minterms Because an n-input decoder generates all of the minterms of n variables, n-variable functions can be realized by ORing together selected minterm outputs from a decoder

6. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 6 An encoder performs the inverse function of a decoder E.g. 8-to-3 priority encoder If more that one input is 1, the highest number determines the output D is 1 if any input is 1, otherwise d is 0

7. Department of Communication Engineering, NCTU 7 2.2 Register and Register Transfers

8. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 8 A 4-bit register is composed of 4 D-type FFs which share a common clock, clear (Clr) and chip enable (CE)

9. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 9 The symbol notation for a 4-bit register

10. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 10 Data are passed from one register to another. In this case, whether A i or B i is sent to D i depends on En

11. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 11 A 8-bit register with tri-state output enable (En), and its corresponding symbol

12. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 12 Registers use output enable (for releasing data) and chip enable (for accepting data) to transfer data on a bus

13. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 13 Accumulator : the output of adder is fed back as one of a addend

14. Department of Communication Engineering, NCTU 14 2.3 Shift Registers

15. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 15 A shift register is a register whose data can be shifted right or left A 4-bit right-shift register

16. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 16 The timing diagram of a 4-bit right shift register

17. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 17 A right-shift register with inverted rotation feedback Two possible output patterns which depend on the initial state This is called Johnson counter

18. Department of Communication Engineering, NCTU 18 2.4 Design of Binary Counters

19. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 19 A synchronous counter is a counter whose FFs are all driven by a clock. While for a asynchronous counter, the output of FF serves as a driving clock of the next FF A 3-bit synchronous counter implemented with T-FFs

20. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 20 Design the functions of T C, T B, and T A with a state table and a truth table First, draw a stable which lists the present state and the next state, then draw the truth table of the functions

21. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 21 Logic minimizations with the Karnaugh map

22. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 22 For D-FFs, D A is equal to the next state of FF A. So we only need a state table for counters designed with D-FFs

23. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 23 An alternative design with D-FFs

24. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 24 Design of up-down counter The state table and the state graph of a up-down counter

25. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 25 The logic functions of inputs One can verify the function by setting U=0 and D=1, or vice versus. For example, U=0 and D=1

26. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 26 A up-down counter synthesized with D-FFs

27. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 27 Design of loadable counter with count enable

28. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 28 The next-state equations

29. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 29 Design of loadable up-dn counter with count enable? Realize this counter with GAL 22V10 Due on the next meet

30. Department of Communication Engineering, NCTU 30 2.5 Counter of Other Sequences

31. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 31 A five state counter Define the next states of three unused states 001 、 101 、 110 as unspecified The counter can be realized with T-FFs  T =present state’  next state  List the truth table for the next states of  Use the Karnaugh map

32. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 32 Notice that T = Q +  Q So, first design Q + = f (A,B,C) Use Karnaugh map for Q=0 and Q=1, respectively  For Q=0, have T = Q +  For Q=1, have T = (Q + )’

33. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 33

34. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 34 After simplification Notice that even if the next state of 001 ， 101 and 110 are not specified at the beginning, they are assigned certain values implicitly while being used as the don’t care conditions for circuit simplifications

35. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 35 Circuit realization

36. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 36 The effects of don’t care conditions  When CBA=001, T C T B T A = 110, then C + B + A + =111  When CBA=101, T C T B T A = 011, then C + B + A + =110  When CBA=110, T C T B T A = 101, then C + B + A + =011 The final counter

37. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 37 An alternative design with D-FFs This is much easier since D C = C +, D B = B + and D A = A + So, the functions are

38. Department of Communication Engineering, NCTU 38 2.6 Derivation of Flip-Flop Input Equations

39. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 39 In counter design, we mainly derive the input equations of FFs. This can be done either with the true table of the present states and the next states, or with the next-state map

40. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 40

41. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 41

42. Department of Communication Engineering, NCTU 42 2.7 Programmable Logic Array

43. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 43 A programmable logic array (PLA) with n inputs and m outputs is a device that can realize m functions of n variables by means of sum-of-products. A PLA consists of an AND array with n input lines and a OR array with m output lines

44. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 44 An example AND Array OR Array

45. Department of Communication Engineering, NCTU 45 2.8 Programmable Array Logic

46. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 46 Different PLA, the product term of a programmable array logic (PAL) can not be shared by multiple OR gates. Besides, the number of inputs of the OR is fixed and limited, e.g.

47. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 47 A commercial device : GAL20V8B

48. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 48

49. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 49

50. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 50

51. Department of Communication Engineering, NCTU 51 2.9 Programming PAL with ABEL- HDL http://mazsola.iit.uni-miskolc.hu/cae/docs/xabel.html

52. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 52 Basic Boolean operations MODULE and_ff2 TITLE 'And gate and flip-flop' input_1,input_2,Clk pin; input_1,input_2,Clk,reset,!oe pin; output_q pin istype 'reg_d'; Equations output_q.clk = Clk; output_q.ar = reset; output_q.q := input_1 & input_2; output_q.oe = oe; END

53. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 53

54. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 54 Adder MODULE adder TITLE 'full adder block' a, b, cin, sin pin ; sum, carry pin istype ‘com'; Equations sum = ((a & b) $ sin) $ cin; carry = (cin & (a & b)) # ((a & b) & sin) # (cin & sin); END

55. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 55 MODULE mux4to1 TITLE '4 to 1 mux' "Inputs id15..id0 pin; s0,s1 pin; "Outputs y3..y0 pin istype 'com'; "Sets IND = [id15..id12]; INC = [id11..id8]; INB = [id7..id4]; INA = [id3..id0]; YSET = [y3..y0]; SEL = [s1,s0]; Equations YSET = IND & (SEL == 3) # INC & (SEL == 2) # INB & (SEL == 1) # INA & (SEL == 0); END

56. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 56 module sreg8w "Inputs d7..d0, clk, rst, load, l_r, si pin; "Outputs q7..q0 pin istype 'reg'; "Sets DATIN = [d7..d0]; "data input group LSHIFTD = [q6..q0,si]; "output data shifted left, with serial input RSHIFTD = [si,q7..q1]; "output data shifted right, with serial input DATOUT = [q7..q0]; "output data group "Intermediate equations LSHIFT = (l_r == 0); "SHIFT LEFT when s_l is low RSHIFT = (l_r == 1); "SHIFT RIGHT when s_l is high Equations DATOUT := DATIN & load "Load in value if LOAD mode. # LSHIFTD & LSHIFT "Shift data left if LSHIFT mode. # RSHIFTD & RSHIFT; "Shift data right if RSHIFT mode. DATOUT.clk = clk; DATOUT.ar = rst; End sreg8w

57. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 57 MODULE Counter TITLE '4 bit counter circuit' DECLARATIONS clk, !OE pin 1,13; "Clock input rst pin 14 ; "Asynchronous reset preset pin 23; "high value sets count = 1 ld pin 11; "high value sets count = input d3..d0 pin 7,8,9,10 ; "Counter inputs q3..q0 pin 18,17,16,15 istype 'reg'; "Counter outputs data= [d3..d0]; count = [q3..q0]; "Creating output bus EQUATIONS count.clk = clk; "Counter clock input count.ar = rst; "Counter reset input count.ld = preset; "Counter preset to ^h4 count.oe = OE; when ld then count := data; "count = data when ld high, synchrounous load else when !ld then count := count + 1; "Counting when ld low END

58. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 58 MODULE toplev TITLE '8 bit Johnson counter' "Performs an 8 bit Johnson or ring count synchronously. "Inputs CLK,SYSCLR,RUNpin; "Outputs Q7,Q6,Q5,Q4,Q3,Q2,Q1,Q0pin istype 'reg_d,buffer'; "Sets count = [Q7,Q6,Q5,Q4,Q3,Q2,Q1,Q0]; "Counter set. prev = [Q6,Q5,Q4,Q3,Q2,Q1,Q0,!Q7]; "Counter set is fed from this set. "It is much easier to perform wide "operations such as counters or mathematical "functions by establishing signal sets. Equations count.d = prev.q & RUN "increment count if RUN # count.q & !RUN; "hold if not RUN count.clk = CLK; count.ar = SYSCLR; END

59. Hardware Project Unit 2 Review on Logic Elements Sau-Hsuan Wu Department of Communication Engineering, NCTU 59 Bi-directional pin assignment Module biabel //ABEL Description of the Bidirectional Circuit //Input pins: ctrlpin; in1pin; //Output pins: bidir1pin; out1pin; Equations bidir1.oe= ctrl; out1= bidir1.pin; bidir1= in1; end