Long Integer and Float

Question

If a Long Integer and a float both take 4 bytes to store in memory then why are their ranges different?

Answer 1

Integers are stored like this:

• 1 bit for the sign (+/-)
• 31 bits for the value.

Floats are stored differently, giving greater range at the expense of accuracy:

• 1 bit for the sign (+/-)
• N bits for the mantissa S
• M bits for the exponent E

Float is represented in the exponential form: (+/-)S*(base)^E

BTW, "long" isn't always 32 bits. See this article.

Answer 2

Different way to encode your numbers.

Long counts up from 1 to 2^(4*8).

Float uses only 23 of the 32 bits for the "counting". But it adds "range" with an exponent in the other bits. So you have bigger numbers, but they are less accurate (in the lower based parts):

1.2424 * 10^54 (mantisse * exponent) is certainly bigger than 2^32. But you can discern a long 2^31 from a long 2^31-1 whereas you can't discern a float 1.24 * 10^54 and a float 1.24 * 10^54 - 1: the 1 just is lost in this representation as float.

Answer 3

They are not always the same size. But even when they are, their ranges are different because they serve different purposes. One is for integers with no decimal places, and one is for decimals.