ECE 172 Digital Systems. Chapter 2.2 Review: Ring Counter, Johnson Counter. Herbert G. Mayer, PSU Status 7/14/2018

Transcription

1 ECE 172 Digital Systems Chapter 2.2 Review: Ring Counter, Johnson Counter Herbert G. Mayer, PSU Status 7/14/2018 1

2 Syllabus l Ring Counter l Parallel Output Ring Counter l Ring Counter via D Flip-Flops l Timing Diagram of Ring Counter l Johnson Counter l Ring vs. Johnson Counter Table l Pros and Cons 2

3 Ring Counter Pictures and flow of ideas taken from [1] 3

4 Counter l When the output of a shift register array is fed back to its input, result is a ring counter l Data pattern contained within shift register will recirculate as long as clock pulse applied l Constant data pattern will repeat every n clock pulses in n-bit shift register; see below for n = 4 l But necessary first to load some data pattern l Initializing all 0 s or all 1 s doesn t count l How useful is such a simple, continuously looping digital signal pattern? l May be used for counting, count reduction via division, integer modulo operation 4

5 Abstract 4-bit Ring Counter Ring Counter via Shift Registers, 4-bit modulo counter: Possible to Initialize via parallel inputs D A.. D D Or serially via bit-string input at D A 5

6 Ring Counter l Above abstract 4-bit ring counter implemented as sequence of 4 Flip-Flops l May be JK or D Flip-Flops l Initialization may happen serially via D A input, costing 4 separate clock cycles l Or in parallel, costing 1 cycle, via array of inputs D A.. D D l Initial pattern repeats itself every 4 clocks l Number of Flip-Flops 4 is arbitrary, same logic for any number of components l Likely cases 16, 32, or 64 6

7 Abstract 4-bit Ring Counter Abstract Ring Counter, 4 bits, showing parallel outputs. Same repeated pattern of 4 bits every 4 clocks 7

8 Parallel Output Ring Counter l Above abstract 4-bit ring counter functions like the earlier l Yet shows possible parallel outputs Q A.. Q D l In addition to sequential output at Q D of last D Flip-Flop, serially 1 bit per clock cycle l Ring again implemented via direct feedback from last output to first input l If we interpret bit sequence of Flip-Flop as binary number, we d have to invert order of the powers of 2 l Leftmost 1 digit to be viewed lowest power l Bit string is , decimal value: 1, as in 2 0 l Next cycle yields , value: 2, as in 2 1 8

9 Ring Counter via D Flip-Flops Each of 4 bits of Ring Counter via D Flip-Flop: Output Q of FF D back to input D of FF A Read all 4 outputs in parallel Q A.. Q D, or serially at Q D 9

10 Timing Diagram of Ring Counter l Assuming 4 bits and initialization pattern of for 4 bits, input pattern repeats every 4 cycles at output l 5 ½ cycles shown, to emphasize repeat of 1 10

11 Johnson Counter Taken from [2] 11

12 Johnson Counter Def: l A Johnson Counter is a modified ring counter, whose inverted output of last Flip- Flop becomes input to the first l Interestingly, the MOD of the Johnson Counter is 2 * n, with n being number of bits, i.e. number of Flip-Flops used 12

13 Johnson Counter l Named after Robert Royce Johnson, US inventor, l Johnson Counter, AKA Johnson Ring Counter, AKA Twisted Ring Counter l Similar to Ring Counter above l But instead of using the output Q of last D Flop-Flop as input, inverted output Q becomes input of first Flip-Flop l Model here uses 4 Flip-Flops l Initial pattern of of 4 input bits creates 1 output at Q of last (or 4 th ) D Flip-Flop, which is then fed into input of 1 st D Flip-Flop 13

14 Johnson Counter Table Johnson uses inverted output Q D of D Flip-Flop as Feedback into first Flip-Flop Input D 14

15 Johnson Counter Inverted Output Q of FF D into Input D of FF A 15

16 Johnson Counter l Johnson 4-bit ring counter streams blocks of four 0s followed by four 1s l Thus producing an 8-bit pattern with 4 Flip- Flops l Inverted output Q is connected to D input l Thus an 8-bit pattern continually repeats l Example: 1000, 1100, 1110, 1111, 0111, 0011, 0001, 0000, 1000 etc. l Circuit above shows such a Johnson Counter l Next table show Ring- and Johnson Counter 16

17 Ring vs. Johnson Counter Table Ring Counter and Johnson Counter Truth Table: Johnson Counter has 8 States with 4 Flip-Flops! 17

18 Pros and Cons l Johnson Ring counters used in ASIC and FPA design l Goal to create FSAs l Binary counter would required more complex adder circuit, using more components than a ring counter l Adder has higher propagation delay: l Delay steps for adder increase with number of digits l Propagation delay for Ring Counter is nearly constant, regardless of number of bits 18

19 Pros and Cons l Ring Counter can represent only n states, with n = number of bits (Flip-Flops) l Johnson Ring counters can represent 2 * n states l Binary adder can represent 2 n states l Johnson can self-initialize to all 0 state! l Ring- as well as Johnson Flip-Flop only have a limited number states 19

20 Bibliography 1. Wiki for Ring Counter: chpt-12/ring-counters/ 2. Wiki for Johnson counter: seq_6.html 3. Regular and Johnson ring counter together: 4. Robert Joyce Jophnson: en.wikipedia.org/wiki/ Robert_Royce_Johnson 20