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# Logic Design - Chapter 8: counters

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### Logic Design - Chapter 8: counters

1. 1. CHAPTER 8 Counter Circuits 1
2. 2. CLASSIFICATION OF COUNTERS  Asynchronous (ripple)   They use the O/P of one FF to generate the clock transition on another FF (s) Synchronous  clock inputs on each FF are connected together 2
3. 3. CLASSIFICATION OF COUNTERS  Binary  0,1,2, ….,2n –1    0,1,2, …, 10n ‑ 1   i- 0,1, …. 9 ii- 0,1, …99 10 states 100 states Octal   22 states 24 states Decimal   i- 0,1,2,3 ii- 0,1,…,15 0,1,2, .. , 8n-1 Special  Any specified sequence sf states 3
4. 4. CLASSIFICATION OF COUNTERS up  down  up/down  4
5. 5. 3-bit Asynchronous Binary counter : (Mod-8) 5
6. 6. Count sequence Q2 Q1 Q0 0 0 0 0 0 1 toggles at each negative edge of the clock input. 0 1 0 Q1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Q0 toggles at each negative edge of Q0 Q2 toggles at each negative edge of Q1 6
7. 7. Timing diagram of up counters 7
8. 8. DOWN COUNTERS •To form a down – counter simply take the binary outputs from the Q’ outputs instead of the Q outputs 8
9. 9. Timing diagram of down counters • We can alternatively get count-down counter by connecting Q’ of each stage to the negative edge triggered clock pulse of the next stage and get the output from Q output of the flip-flops 9
10. 10. DESIGN OF DIVIDE – BY – N COUNTERS   the frequency of the 22 output line is one-eighth the frequency of the input clock. So, a MOD-8 counter can be used as a divide– 10 by–8 frequency divider
11. 11. A MOD-5 Ripple Binary Counter  the number 5 will appear at the outputs for a short duration, just long enough to Reset the flip-flops. The resulting short pulse on the 20 line is called a glitch. 11
12. 12. Timing Diagram of MOD-5 Ripple Binary Counter  Any modulus counter (divide – by – N counter) can be formed by using external gating to Reset at a predetermined number. 12
13. 13. BCD RIPPLE (DECADE) COUNTER  Counter with ten states in their sequence (modulus –10) are called decade counters. 13
14. 14. 3-decade decimal BCD counter 14
15. 15. SYNCHRONOUS COUNTERS COUNT SEQUENCE A3 A2 A1 A0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 . . . . . . . . 1 1 1 1 FLIP-FLOPS INPUTS TA3 TA2 TA1 TA0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 1 . . . . . . . . 1 1 1 1  TA0 = 1  TA1 = A0  TA2 = A0 A1  TA3 = A0 A1 A2 15
16. 16. SYNCHRONOUS COUNTERS   We can conclude from the excitation table (using a Karnauph map or by inspection that TA0 = 1 TA1 = A0 TA2 = A0 A1 TA3 = A0 A1 A2 16
17. 17. Synchronous Counter Using J-K 17
18. 18. SYNCHRONOUS BINARY DOWNCOUNTER • The only change is that the outputs are used as inputs to the T (or J–K) input of the next flip-flop. 18
19. 19. UP/DOWN SYNCHRONOUS COUNTERS 19