what's the largest number float type can hold?

I'm new to programming and have recently come up with this simple question . float type has 32 bits in which 8 bits are for the whole number part (digits before decimal point). so my question is can float type hold numbers bigger than 255.9999 ?

and I would also appreciate if someone told me why this code is behaving unexpectedly.is it a related issue?

int main(){
float a=123456789.1;
printf("%lf",a);
return 0;
}

for which the output is :

123456792.000000

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The most common 32-bit floating-point format, IEEE-754 binary32, does not have eight bits for a base. The base is fixed at two. It has one bit for a sign, eight bits for an exponent field, and 23 bits for a significand field (a fraction part).

The sign bit determines whether the number is positive (0) or negative (1).

The exponent field, e, has several uses. If it is 11111111 (in binary), and the significand field, f, is zero, the floating-point value represents infinity. If e is 11111111, and the significand field is not zero, it represents a special Not-a-Number "value".

If the exponent is not 11111111 and is not zero, floating-point value represents 2e−127•(1+f/223), with the sign added. Note that the fraction portion is formed by adding 1 to the contents of the significand field. That is often called an implicit 1, so the mathematical significand is 24 bits—1 from the leading 1, 23 from the significand field.

If the exponent is zero, floating-point value represents 21−127•(0+f/223), with the sign added. Note that the leading bit is 0. These are called subnormal numbers. They are included in the format to make some mathematical properties work in floating-point arithmetic.

So the largest finite value represented is when the exponent is 11111110 (254) and the fraction is all ones (223−1), so the number represented is 2254−127•(1+ (223−1)/223) = 2127•(1−2−23) = 2127−2104 = 340282346638528859811704183484516925440.

In float a=123456789.1;, the float type does not have enough precision to represent 123456789.1. (In fact, a decimal fraction .1 can never be represented with a binary floating-point format.) When we have only 24 bits for the significand, the closest numbers to 123456789.1 that we can represent are 123456792 and 123456800.

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what's the largest number [the] float type can hold?

The C Standard defines:

FLT_MAX

Include <float.h> to have it be #defined.

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Comments
  • Yes. Its floating point, not fixed point.
  • float type has 32 bits in which 8 bits are for the whole number part (digits before decimal point) its not the digits before the decimal point. Its the base.
  • Well... you really shoud search SO or wikipedia before asking such questions.
  • The largest value a floating-point type can represent is infinity.
  • See the <float.h> header of your system. It should include FLT_MAX. As of continuation of your question, floating points tend to be less precise when moving far from zero.
  • Comments are not for extended discussion; this conversation has been moved to chat.
  • your answer helped me with all my confusion about float domain .thanks a million