# Designing Counters

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## Introduction: Designing Counters

The art of designing counters is based in sequential circuits and in computational theories. In this last part are contained Mealy and Moore systems to try a countering circuit. In this case, I’m going to utilize Mealy system for the example that I will carry out in the present project.

## Step 1: Planning the Process

I’m going to design a 3-bit counter for counting from 0 to 7 because we will have the following:

2^3 = 8 = {000, 001, 010, 011, 100, 101, 110, 111}

In the Mealy system, we will too have the following:

4 STATES = nodes = a = 00, b = 01, c = 10, d = 11

1 INPUT = x = {0, 1}

1 OUTPUT = y = {0, 1}

ARROWS = x / y

Note: with this system Mealy, you'll save a Flip-flop.

## Step 2: Starting the Process

For designing this counter, you should model and

schematize the process by building a net with nodes in each vertex; for example:

## Step 3: State Tables

For continuing with the design of this counter, you

should set the combination of states and inputs and set the outputs too for generating the equations once you decided which type of Flip-Flop you’re going to use in this project. To this step, you’re going to utilize a state table.

In the following tables, we have:

## Step 4: Using Flip-Flop-T

Once decided that type of flip-flop you want to use, insert a column more in the table #2 for generating the table #4, due to that I will insert the table # 3 for explaining something about flip-flop-T, in which you are going to write the information about the resulting states of your flip-flop in this case the type T. When you have a flip-flop of this type, you should realize that combination of states you will have in the following table:

## Step 5: Table # 4

For generating the table # 4, we‘re going to divide the states by naming them as AB the present states and A’B’ the next states respectively while TA and TB will be referred to resulting states of the flip-flops. That is, the combination of the states from A to A’ and from B to B’ in that order.

## Step 6: Resulting Table # 4

In table # 4, we can observe the following:

X = Y = TB

We have to design this project—two flip-flops (TA, TB).

## Step 7: Using K-Map

In this step, we’re going to simplify the table # 4 through the use of K-Map. Then, for TA, we have the following:

## Step 8: Proceeding to Drawing the Project

In this step, you’re going to take the equations to proceed to draw your project.

Note that in this project, you’ll need to add an NOT gate because X = CLK’. That is, X is equal to CLK complemented. Participated in the
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