Math, asked by manna29, 10 months ago

what is the possibal number with explan​

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Answered by SamikBiswa1911
0

Answer:

If you ask a mathematician, they will tell you that there can’t be such a number because it would break math. If you have a number n, where n is the smallest number after 0, then there can’t be a number n/2, because n is already the smallest. This means that division itself breaks down, which mathematicians don’t like.

If you ask a computer, you will actually get an answer. As opposed to the real world, computers don’t have an infinite amount of numbers because they simply couldn’t fit. Computers store numbers in memory registers, and each register has a fixed number of bits. Imagine if you only had three digits. The biggest number you could represent would be 999. This is what happens in a computer.

This means that the set of integers in a computer is limited by the number of digits. In a computer, there is definitely a largest number (for instance, INT_MAX in C). It's the number with the maximum amount of digits, all of which are set to a binary 1. On an 8-bit system, this number would be 11111111.

We can complicate matters even more by including negative numbers. If we have 8 bits of data, we can use the first bit to represent the sign of the number. 0 for plus and 1 for minus. Now we have 7 bits for our digits, so the biggest number is 011111111 which is smaller than our previous biggest number.

We’re still not done. We also need to represent decimal numbers. Even if 0.12 is a small number, it still has three digits, just like 123. The difference is there’s one more thing we need to think about: the decimal dot, also called the radix point. We need to store both the digits, and the position of the radix point.

While integers are limited in how large they can be, decimal numbers are limited in both size and precision. If you have a fixed number of digits, there’s only so many digits you can put after the decimal dot. This is why computers need to round decimal numbers.

How do we store these decimal numbers, then? Computers only understand integers, so we need a way to store a decimal number only using integers.

Say we have the number 3.14. Let's start by writing our all the digits of the number. We get 314. That's a start. We know that by multiplying by powers of 10, we can "move" the decimal point around the number. 314 * 10^-1 is 31.4, while 314 * 10^-2 is 3.14.

All we need to represent the number 3.14 is three integers: 314, 10 and -2. 314 is what’s called a significand, and this is all the digits of the number written out.

10 is called a radix or a base. We know that by multiplying with powers of 10 we can move the decimal dot around numbers in base 10. The same works for all number bases: in base 2 (or binary), you can shift the dot by multiplying by powers of 2.

The power we shift by is called the exponent, and it tells us where the decimal dot is.

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