# 3 bit synchronous counter mod (solved)

#### Random3s

Joined Jul 30, 2014
38
Hi all,

This is a text book question from a study course. Its asks to modify a 3 bit synchronous counter by inverting the output so that it matches the truth table below:

A B C X
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 1

I have minimised the truth table using Karnaugh tables and find that X = A/B+AC and have drawn the circuit attached.

There are probably many ways of achieving this, but as I am fairly new the dig logic topic I am sticking with simplicity.

I am unsure about my results, as its a counter circuit, which needs the output changed, is it ok to add gates, or should I be looking at trying to design a counter circuit which reproduces the truth table somehow?

Id appreciate any helpful input thanks.

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#### tshuck

Joined Oct 18, 2012
3,534
[...]
A B C X
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 1

[...]
This isn't a truth table for a counter circuit. You need to specify what the count should go to from the current state, unless this is preempted by saying it is a linear counter (which would be poor form IMO, as this is a study class, which should be more rigorous).

Assuming the count is linear, you no longer have a counter, but a finite state machine (FSM), where the outputs are dependent on the current state only (a Moore machine, as opposed to a Mealy type FSM, whose output is dependent on current state and inputs).

If this is the case, your output is only decoding the current state (outputs from the flip flops) in order to match the output given in the truth table.

#### Random3s

Joined Jul 30, 2014
38
Thanks for taking the time to comment.

This is a distance learning course I am doing, and unfortunately it's often difficult to get clarification on ambiguous points. This circuit is an expansion from a 3 bit synchronous up counter, which was a previous circuit build.

As far as I understand the task, I need to redesign the 'circuit' so that the output is the same as the truth table, separate from the counter circuit.

I think as part of my original post I was asking for someone to decipher the question for me too. As far as creating a logic circuit to match output x, i seem to have achieved that, but I think I wanted to hear that I've done it correctly.

Thanks again for helping out.

#### WBahn

Joined Mar 31, 2012
26,398
When you say you are supposed to invert the output, what output are you talking about and what do you mean by invert? What is X in your table? What logic operation are you using the division symbol for? Negation? If so, are you inverting the symbol after the operator or before?

#### Random3s

Joined Jul 30, 2014
38
When you say you are supposed to invert the output, what output are you talking about and what do you mean by invert?
That is a very good question, and I wish I could give you a precise answer, I am actually still waiting for clarification on what the task is asking me to do.

I used division / to symbolise not b. So my minimisation of the truth table resulted in A(not)B+AC.

The whole task asked me to building a 3 bit synchronous up counter, using an sr latch as clk input. After this it asks me to 'redesign' the circuit so that the output is 'inverted' as per the truth table (provided above), X being the desired output.

I am assuming that the task is to use the outputs of the jk flipflops, in order to produce output x. To be fair some of the course material has caused ambiguity in the past. I wouldnt be surprised if the question should sound more like "DESIGN a circuit using the truth table below, and use logic minimisation to build the simplest possible circuit".

Finite state machines etc have not been covered thus far, Ive had a read of the materials in the learning section here, and I understand the concept; but certainly not all the theory.....just yet

I think something which confuses me at the moment, is the design of finite state machines, am I right in saying that if I was expected to produce a finite state machine, I would be given a state diagram or a series of actions.. truth tables are generally for building combinational logic right?