# Thread: How many numbers can a 16-bit system represent? Show your working.

1. How many numbers can a 16-bit system represent? Show your working.
Im not trying to cheat by asking others to help me in my homework...
but i find this a really wierd question.

2) why arent there any specifications to what base i am supposed to give the answer in? what should i assume?
3) why arent there any specifications to whether its signed or unsigned? what should i assume?

so which is the correct answer?
1)
A 16-bit system can represent 655351 signed numbers.
The largest a 16-bit system can represent is 1111 1111 1111 1111
(then i do the calculations)
2)
A 16-bit system can represent 1310711 unsigned numbers.
The largest a 16-bit system can represent is 1111 1111 1111 1111
(then i do the calculations)
3)
A 16-bitsystem can represent 1111 1111 1111 1111₂ Show your working part...... (i dont get what i supposed to do in this step)
4)
or what?

2.

3. I think that understanding what a 'bit' is and what 'signed/unsigned' means would get you most of the way to answering your questions.

How would you (in your own words) describe a 'bit'?
What does (in your own words) 'signed/unsigned' mean?

4. Originally Posted by ryanawe123
2) why arent there any specifications to what base i am supposed to give the answer in? what should i assume?
If someone asked how many bananas you had, would you ask what base they wanted the answer in? Why is this any different. I would always answer a "how many" question with the generally accepted type of number (base 10). If you want to use examples of binary code to explain why you have come up with the answer then that is reasonable.

3) why arent there any specifications to whether its signed or unsigned? what should i assume?
Why would this change the number of values that can be represented? It may change the range of of numbers that can be represented (i.e. either "between 0 and some large positive integer" or "between some large negative number and some large positive number"). But it could be fixed point, representing values between 0 and 1 (possibly also signed). This still doesn't change the number of values that can be represented, just what those values are.

so which is the correct answer?
Not telling. (Actually: none of them)

"Show your working" is an odd phrase in this context. I would have said something like "and explain why" ...

I would approach it by using the example of, say, a 2 bit number where all the possible values can be listed and then use as an example of the general rule to calculate how many values can be represented by n bits and then show the result for n = 16.

1) A 16-bit system can represent 655351 signed numbers.
The largest a 16-bit system can represent is 1111 1111 1111 1111
(then i do the calculations)
If you say that, make sure you explain under what circumstances that is the largest value (bearing in mind your Q3 above).

2) A 16-bit system can represent 1310711 unsigned numbers.
The largest a 16-bit system can represent is 1111 1111 1111 1111
(then i do the calculations)
Could you explain where you get 131071 from? Especially as you show the same maximum number...

3) A 16-bitsystem can represent 1111 1111 1111 1111₂ Show your working part...... (i dont get what i supposed to do in this step)

So, it seems maybe you are confusing "the maximum value that can be represented" and "the number of values that be represented"?

5. Originally Posted by Strange
So, it seems maybe you are confusing "the maximum value that can be represented" and "the number of values that be represented"?
isnt they the same? :O

6. Originally Posted by ryanawe123
Originally Posted by Strange
So, it seems maybe you are confusing "the maximum value that can be represented" and "the number of values that be represented"?
isnt they the same? :O
OK. So do what I suggested and take a 2 bit number and write down all possible values. Compare the largest value (assume unsigned integers, for simplicity) with the number of values you have written down. Explain the difference.

Or, if that is confusing, write down all the values that can be represented by a single decimal digit and compare the number of those values with the largest value....

7. oh i think i get it...

"range of signed values" vs "maximum unsigned value" are different. is that what you are saying?

8. Originally Posted by ryanawe123
oh i think i get it...

"range of signed values" vs "maximum unsigned value" are different. is that what you are saying?
That is certainly true. But also "range of UNsigned values" vs "maximum unsigned value" are different. (Where "range" in this context means the number of different values that can be represented)

How many decimal digits are there? Therefore how many different values can be represented by a single digit? But what is the largest value that can be represented by a single digit? Are these the same or not?

9. is there any online octal-to-hexadecimal-direct-conversion-with-steps website?

10. Question:
How many numbers can a 16-bit system represent?
so, to answer this question, im guessing either
unsigned(1111 1111 1111 1111₂)
65535
Working...? what working?

11. Originally Posted by ryanawe123
Question:
How many numbers can a 16-bit system represent?
so, to answer this question, im guessing either
unsigned(1111 1111 1111 1111₂)
65535
Is 0 (zero) a number?

12. Originally Posted by ryanawe123
Question:
How many numbers can a 16-bit system represent?
so, to answer this question, im guessing either
unsigned(1111 1111 1111 1111₂)
65535
This answer (it is one answer given in two different forms) is wrong.

Please try and answer these questions: How many decimal digits are there? Therefore how many different values can be represented by a single digit number? But what is the largest value that can be represented by a single digit number? Are these the same or not?

I am trying to get you to work through this because it is a really important point to understand. You won't learn if someone just tells you the answer; you need to understand why it is the answer.

13. Strange, are decimals (the dot symbol) be included in the binary system? if so then there are lots lots more than just 65535

14. Originally Posted by Strange
How many decimal digits are there?

9 digits
Therefore how many different values can be represented by a single digit number?
9 values
But what is the largest value that can be represented by a single digit number?
9
Are these the same or not?

its the same,

I am trying to get you to work through this because it is a really important point to understand. You won't learn if someone just tells you the answer; you need to understand why it is the answer.
.......

15. then why did the question specify: "a 16-bit system"?

16. Originally Posted by ryanawe123
Originally Posted by Strange
How many decimal digits are there?
9 digits
Really? Can you list them?

17. Originally Posted by ryanawe123
how many decimal digits are there?

9 digits
lol

18. hold on its wrong let me try again.

19. Originally Posted by ryanawe123
then why did the question specify: "a 16-bit system"?
How many values can a decimal number represent in one digit?

How many values can a decimal number represent in two digits?

How many values can a decimal number represent in three digits?

Similarly, the number of different values that can be represented by two binary digits is smaller than the number that can be represented in 8, 16 or 32 bits.

20. Originally Posted by Strange
How many decimal digits are there?

10
Therefore how many different values can be represented by a single digit number?
9
But what is the largest value that can be represented by a single digit number?
9
Are these the same or not?

10,9,9 different.

I am trying to get you to work through this because it is a really important point to understand. You won't learn if someone just tells you the answer; you need to understand why it is the answer.
dfghsdfg

21. Originally Posted by Strange
Originally Posted by ryanawe123
then why did the question specify: "a 16-bit system"?
How many values can a decimal number represent in one digit?
10
How many values can a decimal number represent in two digits?
100
How many values can a decimal number represent in three digits?
1000
Similarly, the number of different values that can be represented by two binary digits is smaller than the number that can be represented in 8, 16 or 32 bits.
oh... i hope i got it.
what i got was...
How many numbers can a 16-bit system represent? Show your working.
it included zero............................
AM I RIGHT?

it still wrong -_-

22. Banzai!

Now. Does that with the answer to the question about 16 bit binary? (Think about why the maximum vale and the number of values is different <cough>zero<cough>)

23. unsigned(10000000000000000₂)

or

65536

RIGHT RIGHT DD

24. Originally Posted by RedPanda
Is 0 (zero) a number?
I guess I am on ryanawe123's ignore list.

25. zero is a word. 0 is a number.

26. Originally Posted by ryanawe123
zero is a word. 0 is a number.
Really?
Really?!