CODEWITHSUNDEEP
cbinary
Sheldor
Sheldor

Reputation: 310

How to distinguish a negative binary number?

Suppose I am dealing with 4 bit operations. So if I encounter an binary digit say 

1111

then what should I infer ? Is it -1 or 15 ?

Upvotes: 3

Views: 174

Answers (1)

unwind
unwind

Reputation: 399833

"That depends".

The bits are (in this case) encoding a number, but you have to know which kind of number (signed or unsigned, integer, fixed-point or float) in order to interpret the encoded bits.

If the number is supposed to be signed in two's complement, then the proper interpretation is -1, if it's unsigned then it's 15.

It's not possible to decide from those four bits alone, it's simply not enough information.

This of course is true for a "full-sized" value too, it could be an int or an unsigned int and you have to know that in order to correctly interpret the bits.

Update: If you know that your number is supposed to be signed, the easiest way to deal with it (assuming C, which generally doesn't have a signed 4-bit integer type) is to sign-extend it into a usable form.

Sign-extending merely involves taking the most significant bit of the fewer-bits number, and repeating it to the left up to (and including) the most significant bit of the target one.

So in your case, you have 0xf, whose top bit is 1. Extending to an int8_t, we get:

const int8_t number = 0xff;

Which is -1.

There is no built-in way to do this sign-extension from an arbitrary few-bits number, since C can't natively deal with those.

Here's a naive approach:

// Sign-extend a n-bit number into 32 bits.
int32_t extend(uint32_t bits, size_t n)
{
  const bool top = bits & ((uint32_t) 1 << (n - 1));
  if (top)
  {
    for (size_t i = n; i < 32; ++i)
      bits |= 1 << i;
  }
  return bits;
}

If you call the above with your number:

printf("%d\n", (int) extend(0xf, 4));

it prints -1.

Upvotes: 2

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