How can I set normal clock input?

Question

input

  clk ( clock ) :

        0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ...

required output :

   F   :
        0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 ...

How can I get that output over using combinational and sequential circuit (logic gate and flip-flop) ? Can you recommend any topic or web-page ?

Answer 1

Well, the sequence repeats after every 8 bit: 0 0 1 1 0 0 0 0. Now log_2(8)=3, this means you need 3 element counter with output function:

0 0 0 = 0
0 0 1 = 0
0 1 0 = 1
0 1 1 = 1
1 0 0 = 0
1 0 1 = 0
1 1 0 = 0
1 1 1 = 0

Now I personally use :

fun = BooleanMinimize[
  BooleanFunction[{{0, 0, 0} -> 0, {0, 0, 1} -> 0, {0, 1, 0} -> 
      1, {0, 1, 1} -> 1, {1, 0, 0} -> 0, {1, 0, 1} -> 0, {1, 1, 0} -> 
      0, {1, 1, 1} -> 0}][c, b, a]]

with an output of: b && ! c, but you could use Karnaugh map.

Now you can search wolframalpha.com for: logic circuit b && ! c.

So now you need to make 3 JK-triggers to make 3 element counter, with outputs {a, b, c} and you only need b and c output. You can look up your lecture notes to see how to connect them up.

Simple 4 bit 2 way counter using JK-triggers and some binary logic.

• Upper and operator path is used when counting up.
• When counting down path below is used.
• or elements are used to combine them.
• Extra logic input and inverse is used to determine what way to count.

Answer 2

do you see the pattern in the output ? it is almost 0 0 1 1 0 0 1 1 0 0 1 1 0 0 .... what does it looks like ?

hint: count the clock, represent the count as a binary number...

now that you can get the above output from your clock, see if you cannot get another bit which you could use to cancel the previous output in order to get the desired output.

hint: look further in the above hint...

Answer 3

The circuits on this page should help, http://www.play-hookey.com/digital/synchronous_counter.html

The 'A' state is the same as your clock: