# 3 bit synchronous counter design d flip flop

Any idea how I would go about designing a 3 bit synchronous counter in regards to having the following states

111->001->110->101->100->000->010->111


I drew up a present state and next state table etc... not really sure where to go from here, I have designed in logism a start schematic with a CLK, CLR and PRE, with 3 D type Flip flops as these are the ones I am required to use, but I am unsure where to go from here.

The key thing is to treat each bit individually.

For example, for the low-order bit, lets call it next_state[0].

state     | next_state[0]
---------------
000    | 0
001    | 0
010    | 1
011    | X
100    | 0
101    | 0
110    | 0
111    | 1


So you can write

next_state[0] = state[0] & state[1] & state[2] | ~state[0] & state[1] & ~state[2]

If you are building this with discrete logic you could simplify this to

next_state[0] = state[1] & (state[0] & state[2] | ~state[0] & ~state[2])

And you have an equation you can use to drive the flip-flop that will generate the next condition for the low-bit of the state variable.

Finding the equations for the other two state bits works the same way.

• i must be missing something, how do you know 010 = 1? i'm lost in regards to how you got that table
– Sim
Commented Mar 16, 2013 at 5:33
• According to your question, when the current state is 010, the next state is 111, which means the low bit is 1. Commented Mar 16, 2013 at 5:39
• can i use a 3 k maps for each different state?
– Sim
Commented Mar 16, 2013 at 6:04
• Yes Karnaugh is the way to go here. Or a small microcontroller. Commented Mar 16, 2013 at 8:55
• @Sim, one k-map for each bit of next_state is enough. Commented Mar 16, 2013 at 15:57