EKT 221 : Digital 2 COUNTERS

1. EKT 221 : Digital 2COUNTERS

2. Synchronous Counter • To eliminate the "ripple" effects, a common clock pulse for each flip-flop and a combinational circuit are used to generate the next state. • For an up-counter (counts up by 1), an incrementer is used.

3. Synchronous Counter

4. Synchronous Counter Serial Gating

5. Synchronous Counter • Internal Logic • XOR complements each bit • AND chain causes complement of a bit if all bits toward LSB from it equal 1 • Count Enable • Forces all outputs of AND chain to 0 to “hold” the state • Carry Out • Added as part of incrementer • Connect to Count Enable of additional 4-bit counters to form larger counters

6. Binary Counter with Parallel Load • Add path for input data, Di • enabled for Load = 1 • Add logic to : • Disable count logic for Load = 1 • Disable feedback from outputs for Load = 1 • Enable count logic for Load = 0 & Count = 1

7. Binary Counter with Parallel Load • The resulting function table :

8. Load 4-bit Binary Counter with Parallel Load Count Carry Output, CO Clock

9. Converting parallel load counter into synchronous BCD counter • Connect an external AND gate to LOAD • Counter starts with all-zero output (0000) • COUNT input always HIGH (1)

10. Converting parallel load counter into synchronous BCD counter • AND gate = 0 (LOAD = 0), BCD counts from 0000 to 1001 • Output = 1001, Q0 and Q3 in HIGH, AND gate = 1 (LOAD = 1) • Next clock transition, counter load inputs (D0  D3) = 0000 following 1001 into counter. 1 1 1 1 0 0 0 0 0 1 0

11. Converting parallel load counter into synchronous BCD counter Y

13. Synchronous BCD Counter • Y = 1, when present state = 1001 • FF input equations • Obtained from next – state values • Simplify using K – map • 1010 ~ 1111  don’t care • Y = Q1Q8

14. Modulo – N Counter • A counter that goes through a repeated sequence of N states • Maximum decimal number to be counted : • If Mod N = 2n then the max decimal counted is N-1 • If Mod 16, then the max decimal number is 15 • To determine the required number of flip-flops: • n flip-flop 2n output = Mod N

15. Modulo – 7 Counter • Use a synchronous 4 – bit binary counter with a synchronous LOAD and C • LOAD – detect count “6” and load “0” • Gives count of (0, 1, 2, 3, 4, 5, 6, 0, 1, …) • Using don’t care for states above 0110 • Detect number “6” when LOAD = Q2Q1

16. Modulo – 7 Counter 1 0 0 0 0 0 1 1 0 0 0 0 0 1

17. Modulo – 6 Counter : Special requirement • Requirement: Synchronously preset “9” on RESET and LOAD “9” on terminal count “14” • Use a synchronous, 4 – bit counter with a synchronous LOAD • Use LOAD signal to : • preset count to “9” • detect count “14” • Give count of (9, 10, 11, 12, 13, 14, 9, 10, …)

18. Modulo – 6 Counter : Special requirement Synchronously preset “9” on RESET and LOAD “9” on terminal count “14” 1 1 1 1 0 1 1

19. Arbitrary Count Sequence • Design a counter with sequence of six states as in Table 7-10

20. Arbitrary Count Sequence • 2 states are not included : 011 and 111 • Simplified equations :

21. Arbitrary Count Sequence • Logic diagram of the arbitrary counter

22. THE END