Binary Woes

Æthelred

This is really going to look like a homework question, but I swear 'tisn'.t.

I'm looking at a past exam paper for Computer Science and the question is thus:

"Show how it is possible to represent the decimal number 1024 as an 8 bit binary number."

Now, to me, this seems impossible. 1024 in binary is: 0100 0000 0000 .. and that needs 11 bits. I don't see how to express the number in a lower amount of bits. Is it something to do with floating points..?

jclast

There is no reason that you couldn't store it as 0100 0000 as long as whatever is accessing it knows to multiply the stored value by 0001 0000 when it needs to use the value. Of course you lose precision this way (can only store multiples of 16), but I can't see any other way to do it.

Æthelred

That's a solution, yeah. It's hard to know where the question is coming from. I'm not sure if that would be an acceptable answer or not. You could just as well say "have a program set to interpret 0001 as 1024", surely.

GothicLargo

Æthelred wrote: »

This is really going to look like a homework question, but I swear 'tisn'.t.

I'm looking at a past exam paper for Computer Science and the question is thus:

"Show how it is possible to represent the decimal number 1024 as an 8 bit binary number."

Now, to me, this seems impossible. 1024 in binary is: 0100 0000 0000 .. and that needs 11 bits. I don't see how to express the number in a lower amount of bits. Is it something to do with floating points..?

You are obviously correct that in a flat binary tally, it is impossible to count to 1024 in 8 bits. So in some sense you will need to think like a cheater.

No, I'd instead say that there exists in memory an array of length <=256 which contains 32 bit numbers and that 1024 is in that array. The 8 bit number X is the index number which points to 1024 in that array. Boom, you've just "represented" 1024 using 8 bits by saying that the representation is a pointer.


"By putting it in 8-bit addressed memory."

Æthelred

Ah, that's quite cunning. Again, though, I'm not sure if it'd be allowed.. this isn't a programming paper; the question is surrounded by simple "convert to two's complement" questions and so on. It's possible it's a semi-trick question, but that'd be kind of a dick move for question 1b on an entry-level paper.

I think I will have to see if I can get the "approved" answer to clear this up. Thanks.

edit:

question setter wrote:

It's to do with the use of scientific notation in computers (as in 6.022*10^23).

Clipse

Æthelred wrote: »

Ah, that's quite cunning. Again, though, I'm not sure if it'd be allowed.. this isn't a programming paper; the question is surrounded by simple "convert to two's complement" questions and so on. It's possible it's a semi-trick question, but that'd be kind of a dick move for question 1b on an entry-level paper.

I think I will have to see if I can get the "approved" answer to clear this up. Thanks.

edit:

question setter wrote:

It's to do with the use of scientific notation in computers (as in 6.022*10^23).

In a semi-scientific-notation style you could, for instance, use 4 bits as an exponent (of 2) and the other 4 as the value. So, for instance, if the second 4 bits are the exponent, 1024 would be 0001 1010, since it is 1*2^10. It's kind of an open-ended question with the value they chose, since you could just as easily have used 5, 6, 7, or even 8 bits for the exponent.

PeregrineFalcon

Clipse wrote: »

Æthelred wrote: »

Ah, that's quite cunning. Again, though, I'm not sure if it'd be allowed.. this isn't a programming paper; the question is surrounded by simple "convert to two's complement" questions and so on. It's possible it's a semi-trick question, but that'd be kind of a dick move for question 1b on an entry-level paper.

I think I will have to see if I can get the "approved" answer to clear this up. Thanks.

edit:

question setter wrote:

It's to do with the use of scientific notation in computers (as in 6.022*10^23).

In a semi-scientific-notation style you could, for instance, use 4 bits as an exponent (of 2) and the other 4 as the value. So, for instance, if the second 4 bits are the exponent, 1024 would be 0001 1010, since it is 1*2^10. It's kind of an open-ended question with the value they chose, since you could just as easily have used 5, 6, 7, or even 8 bits for the exponent.

Or you could store it as (first four bits)^(last four bits) and get 0010 1010 (2^10)

Or get bitwise on them and write it as 0100 0000 << 4

Clipse

PeregrineFalcon wrote: »

Clipse wrote: »

Æthelred wrote: »

Ah, that's quite cunning. Again, though, I'm not sure if it'd be allowed.. this isn't a programming paper; the question is surrounded by simple "convert to two's complement" questions and so on. It's possible it's a semi-trick question, but that'd be kind of a dick move for question 1b on an entry-level paper.

I think I will have to see if I can get the "approved" answer to clear this up. Thanks.

edit:

question setter wrote:

It's to do with the use of scientific notation in computers (as in 6.022*10^23).

In a semi-scientific-notation style you could, for instance, use 4 bits as an exponent (of 2) and the other 4 as the value. So, for instance, if the second 4 bits are the exponent, 1024 would be 0001 1010, since it is 1*2^10. It's kind of an open-ended question with the value they chose, since you could just as easily have used 5, 6, 7, or even 8 bits for the exponent.

Or you could store it as (first four bits)^(last four bits) and get 0010 1010 (2^10)

Or get bitwise on them and write it as 0100 0000 << 4

Yeah there is basically an infinite* number of ways to solve the problem, but with the scientific notation hint I'd imagine they're trying to make it vaguely similar to how floating point data is stored.

* - Ok, 256 ways, but with infinitely many explanations.

PeregrineFalcon

Clipse wrote: »

Yeah there is basically an infinite* number of ways to solve the problem, but with the scientific notation hint I'd imagine they're trying to make it vaguely similar to how floating point data is stored.

* - Ok, 256 ways, but with infinitely many explanations.

This made me chuckle. They're probably just trying to see how you'll answer it, and any of them will be perfectly valid.

Dick answer follows:
You could say that x is 0100, and your program automatically bitshifts everything left by itself twice. :P