The same as real numbers are expressed in decimal, except only the digits 0 and 1 are used (instead of 0 to 9) and the separator between the integer and fraction part is called the binary point (instead of the decimal point). The sign if needed is the same as in decimal.
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Expressed in decimal, the sum of the numbers 1 to 8192 is 33558528 - expressed in binary, this number is equal to 10000000000001000000000000.
All decimals are real numbers and all real numbers can be expressed as decimals.
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. NOt all real numbers are rational.
All real are rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
All irrational numbers are real, but not all real numbers are irrational.