BCD up Counter
Cuthbert Nyack
A simple application of a digital electronics sequential circuit is shown below.
It is a BCD up counter using J/K flip-flops. The flip-flops have internal
AND gates which AND'S all the inputs to the J or K inputs.
Clicking on the CLOCK tab changes the state of the counter
(state changes when mouse button is released). At any time the flip-flops can
be cleared by clicking on the CLEAR tab. Note the J and K inputs before
each clock pulse and how the flip-flop changes.
Blue corresponds to LOW and red to HI. LSB is A and MSB is D.
The table below shows the changes that take place
when a clock pulse arrives with the J and K values indicated.
Output Change For J,K inputs
| J input |
K input |
Output Change |
| 0 |
x |
0 ® 0 |
| 1 |
x |
0 ® 1 |
| x |
1 |
1 ® 0 |
| x |
0 |
1 ® 1 |
From the above table a new table can be drawn up showing the values required
at the J and K inputs for each clock pulse. To go from count 0 to count
1, D, C and B must
remain at 0. From above table this means J(D) = J(C) = J(B) = 0 and
K(D) = K(C) = K(B) = x. The least significant bit A must change from 0 to 1. From above table
this means J(A) = 1 and K(A) = x. This gives the first row of the
table below.
Table of J,K inputs for required output change in D,C,B and A
| Count |
|
D |
C |
B |
A |
|
J(D) |
J(C) |
J(B) |
J(A) |
|
K(D) |
K(C) |
K(B) |
K(A) |
| 0 |
|
0 |
0 |
0 |
0 |
|
0 |
0 |
0 |
1 |
|
x |
x |
x |
x |
| 1 |
|
0 |
0 |
0 |
1 |
|
0 |
0 |
1 |
x |
|
x |
x |
x |
1 |
| 2 |
|
0 |
0 |
1 |
0 |
|
0 |
0 |
x |
1 |
|
x |
x |
0 |
x |
| 3 |
|
0 |
0 |
1 |
1 |
|
0 |
1 |
x |
x |
|
x |
x |
1 |
1 |
| 4 |
|
0 |
1 |
0 |
0 |
|
0 |
x |
0 |
1 |
|
x |
0 |
x |
x |
| 5 |
|
0 |
1 |
0 |
1 |
|
0 |
x |
1 |
x |
|
x |
0 |
x |
1 |
| 6 |
|
0 |
1 |
1 |
0 |
|
0 |
x |
x |
1 |
|
x |
0 |
0 |
x |
| 7 |
|
0 |
1 |
1 |
1 |
|
1 |
x |
x |
x |
|
x |
1 |
1 |
1 |
| 8 |
|
1 |
0 |
0 |
0 |
|
x |
0 |
0 |
1 |
|
0 |
x |
x |
x |
| 9 |
|
1 |
0 |
0 |
1 |
|
x |
0 |
0 |
x |
|
1 |
x |
x |
1 |
From above Table one can immediately see that J(A) = K(A) = 1.
Karnaugh maps for J(B) and K(B) are shown below.
Karnaugh maps are obtained by representing each column of the above table
in a 4 variable Karnaugh map. Values from 10 to 15 are represented by don't
care x states. The map for J(B) is shown in the table below.
Karnaugh Map for J(B)
| |
!A |
A |
A |
!A |
|
| !B |
0 |
1 |
1 |
0 |
!D |
| B |
x |
x |
x |
x |
!D |
| B |
x |
x |
x |
x |
D |
| !B |
0 |
0 |
x |
x |
D |
| |
!C |
!C |
C |
C |
|
| J(B) = A!D |
Using squares with orange
letters and light blue background gives J(B) = A!D.
Karnaugh Map for K(B)
| |
!A |
A |
A |
!A |
|
| !B |
x |
x |
x |
x |
!D |
| B |
0 |
1 |
1 |
0 |
!D |
| B |
x |
x |
x |
x |
D |
| !B |
x |
x |
x |
x |
D |
| |
!C |
!C |
C |
C |
|
| K(B) = A |
Using squares with orange
letters and light blue background gives K(B) = A.
Similar analysis shows
J(C) = AB, K(C) = AB, J(D) = ABC and K(D) = A.
Return to main page
Return to page index
COPYRIGHT © 1996 Cuthbert A. Nyack.