# 2 bit binary counter karnaugh diagram

Discussion in 'Homework Help' started by hadoque, Nov 8, 2009.

Jul 24, 2007
10
0
Hi
I'm supposed to design a 2 bit binary counter with an extra input, x, to decide whether it should count up or down (x=1 counts up). The design uses two D-flip-flops.
To help I got a couple of truth tables to fill in. The first is for both flip-flops, D1 and D2. Then this one is split to two separate tables, for each flip-flop.
q1 is the output of the D1 flip-flop and so forth.
This is how I filled the tables:
Code ( (Unknown Language)):
1.
2. q1q2|x=0|x=1
3. ____|___|___
4. 00  | 11|01
5. ____|___|___
6. 01  | 00|10
7. ____|___|___
8. 11  | 10|00
9. ____|___|___
10. 10  | 01|11
11. ____|___|___
12.
13.      D1 D2
14.
15. q1q2|x=0|x=1
16. ____|___|___
17. 00  |  1|  1
18. ____|___|___
19. 01  |  0| 0
20. ____|___|___
21. 11  |  0| 0
22. ____|___|___
23. 10  |  1| 1
24. ____|___|___
25.
26.      D1
27.
28. q1q2|x=0|x=1
29. ____|___|___
30. 00  | 1 |0
31. ____|___|___
32. 01  | 0 |1
33. ____|___|___
34. 11  | 1 |0
35. ____|___|___
36. 10  | 0 |1
37. ____|___|___
38.
39.      D2
40.
When I collect the ones to make the boolean functions, I get:

Code ( (Unknown Language)):
1.
2. D1 = q1' + q2'
3. D2 = x'q1'q2' + xq1'q2 + x'q1q2 + xq1q2'
4.

2. ### Thav Member

Oct 13, 2009
82
0
How does D2 equal 1? It looks correct to me. Your equation for D1 is off, however.