Digitial Logic and Binary Counter

In summary, the clock signal starts with a 1 and the counter starts at 000 because it has not flipped yet.
  • #1
ver_mathstats
260
21
Homework Statement
We are required to find the output of a three-bit binary counter when the input is 1100101001.
Relevant Equations
input: 1100101001
10000
10000
00011
00011
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.

00000
00000
10011
00011
10102

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.
 
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  • #2
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 ?
 
  • #3
Baluncore said:
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.
 
  • #4
ver_mathstats said:
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.

ver_mathstats said:
... 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.
 
  • #5
Baluncore said:
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?
 
  • #6
ver_mathstats said:
... , now my only issue is still trying to determine if I start at 000 which I am going to assume yes?
ver_mathstats said:
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).
Correct. If the initial condition of a circuit is not clearly identified in the question, you must state that, and specify your assumption clearly.
 
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  • #7
Baluncore said:
Correct. If the initial condition of a circuit is not clearly identified in the question, you must state that, and specify your assumption clearly.
Thank you very much, I got it now
 

FAQ: Digitial Logic and Binary Counter

1. What is digital logic?

Digital logic is a type of logic that deals with the representation and manipulation of signals or data that can only have two possible values: 0 or 1. It is the foundation of all digital electronic systems and is used to design and build digital circuits and systems.

2. What is a binary counter?

A binary counter is a digital circuit that counts in binary from 0 to 2^n-1, where n is the number of bits in the counter. It is commonly used to count the number of clock cycles in a digital system and is also used in applications such as frequency division and event counting.

3. How does a binary counter work?

A binary counter works by using a series of flip-flops, each representing a bit in the counter. As the clock signal pulses, the flip-flops change state, resulting in the counter counting up or down in binary. Once the counter reaches its maximum value, it resets back to 0 and starts counting again.

4. What is the difference between synchronous and asynchronous counters?

Synchronous counters use a common clock signal to trigger all the flip-flops at the same time, resulting in all bits changing state simultaneously. Asynchronous counters, on the other hand, use individual clock signals for each flip-flop, resulting in a ripple effect where each bit changes state one after the other.

5. What are the applications of binary counters?

Binary counters have many applications in digital systems, including frequency division, event counting, and sequential logic circuits. They are also used in devices such as digital clocks, timers, and calculators. Additionally, binary counters are essential components in digital signal processing and communication systems.

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