A binary number is a number that belongs to a base-2 numeral system. A base-2 numeral system is a positional system, that is, the value of the number depends on the position the digit has.
We can say that in a base-2 numeral system we can use a zero, and a one or (0 or 1). In this way, we can say that every number at the left of a number is twice the number at the right.
We can also say that if we have the number 1011 in a binary system, we have that its value is equivalent to:
We can say that the small numbers at the top of the number are called an exponent, and these numbers tell us how many times we need to multiply the same number. For example:
We also need to know that if we raise a number to zero (0) the result will be always 1:
In other words, the number 1011 in the base-2 number system is equivalent to 11 in the base-10 numeral system (decimal system) - the system we use every day. By the way, binary numbers are used by computers every day.
We can also see that we only have zeros and ones to represent a number, and depending on where the number is, the value is different. For example, if we switch the number 1 and 0 from their position (using the previous number above), we have a different number:
It is usually to express this equivalence as follows:
Or
In summary, a binary number is also a number, but they use another base to represent it. They use a base-2. Instead, we use a system that uses a base 10 to represent numbers - the decimal system or base-10 numeral system.
The binary numbers are used by computers and we all humans use base-10 numbers in our daily lives. It is important to remember that binary numbers are also part of a positional system - each value of the number depends on the position the digit has.