# Digitial Logic and Binary Counter

ver_mathstats
Homework Statement:
We are required to find the output of a three-bit binary counter when the input is 1100101001.
Relevant Equations:
input: 1100101001
 1 000 0 1 000 0 0 001 1 0 001 1 1 0 1 0 0 1

On the left is my input, in the middle is my output and on the right is the decimal.

 0 000 0 0 000 0 1 001 1 0 001 1 1 010 2

Here is another example I was studying where the input is 00101 and I understand where each number is coming from and how it operates but I struggle with the first one because the input starts with a 1, so does that mean my counter starts at 000 because it still has not flipped yet? Or does it start at 001 right away because the input begins at 1? So I completed the first three columns and not sure if I am on the right track if someone could tell me that would be appreciated.

Thanks.

## Answers and Replies

2021 Award
What is the initial state of the counter ?
Is it an up or a down counter ?
Is the input a clock signal or an enable clock signal ?
Is the input positive or negative edge advanced ?

ver_mathstats
What is the initial state of the counter ?
Is it an up or a down counter ?
Is the input a clock signal or an enable clock signal ?
Is the input positive or negative edge advanced ?
"A single flip-flop only offers two possible output values: 0 or 1. However, a set of flip-flops can be connected in series to form a binary counter that accumulates a numeric total. Like a flipflop, a counter has a single input. Unlike a flip-flop, however, a counter has multiple outputs. The outputs count how many input pulses have been detected by giving a numerical total in binary†. We think of the outputs as starting at zero and adding one each time the input transitions from 0 to 1. Thus, a counter that has three output lines can accumulate a total between 0 and 7. Figure 2.19 illustrates a counter, and shows how the outputs change when the input changes. In practice, an electronic part that implements a binary counter has several additional features. For example, a counter has an additional input used to reset the count to zero, and may also have an input that temporarily stops the counter (i.e., ignores the input and freezes the output). More important, because it has a fixed number of output pins, each counter has a maximum value it can represent. When the accumulated count exceeds the maximum value, the counter resets the output to zero and uses an additional output to indicate that an overflow occurred." This was given from my textbook. I'm assuming that even though the input starts at 1 the output will be 000, after rereading my textbook.

2021 Award
This was given from my textbook.
The answers to my four questions are in the text you quote.
You need to dig those answers out, before you can solve this type of problem.

... I'm assuming that even though the input starts at 1 the output will be 000, ...
If the clock signal starts with a 1 = "1100101001" then there are two possibilities.
A. The clock signal might be prefixed with many suppressed zeros. 000000001100101001 or;
B. The clock input was set at 1 when the counter was reset and cleared to zero.

Maybe Figure 2.19 contains more information on the initial state of the clock.

ver_mathstats
The answers to my four questions are in the text you quote.
You need to dig those answers out, before you can solve this type of problem.

If the clock signal starts with a 1 = "1100101001" then there are two possibilities.
A. The clock signal might be prefixed with many suppressed zeros. 000000001100101001 or;
B. The clock input was set at 1 when the counter was reset and cleared to zero.

Maybe Figure 2.19 contains more information on the initial state of the clock.
Figure 2.19 is the example I included in the question that I was studying and I understand it completely, the only thing throwing me off "We think of the outputs as starting at zero and adding one each time the input transitions from 0 to 1"? So my attempt I see I already messed up by changing the counter when it went from 1 to 0, now my only issue is still trying to determine if I start at 000 which I am going to assume yes?

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