Binary Formula
Define a binary number system.
A binary number system is a system of numbers that has a base of 2 and uses only two digits, “0 and 1”. It is one of the four types of number systems and is most commonly employed by computer languages like Java and C++. “Bi” in the word “binary” stands for “two.” Some examples of binary numbers are (11)2, (1110)2, (10101)2, and so on.
What is a formula to convert a binary number into a decimal number?
To convert a binary number “an-1….a3a2a1a0“, multiply every digit of the given binary number with the powers of 2.
If the binary number with n-digits is B = an-1….a3a2a1a0,
Now the decimal number is D = (an-1 × 2n-1) +…+(a3 × 23) + (a2 × 22) + (a1 × 21) + (a0 × 20).
What is the formula to convert a binary number into a hexadecimal number?
We have two types of methods to convert a binary number into a hexadecimal number, i.e., by converting binary to hexadecimal directly, and the other one is converting binary to decimal, and then converting the obtained decimal into hexadecimal. To convert the binary number into hexadecimal, we first have to divide the given binary number into a pair of four digits, starting from the right end. Now, substitute the value of the hexadecimal number into it.
What is the formula to convert a binary number into an octal number?
We have two types of methods to convert a binary number into an octal number, i.e., by converting binary to octal directly, and the other one is converting binary to decimal, and then converting the obtained decimal into octal. To convert the binary number into octal, first, we have to divide the given binary number into a pair of three digits, starting from the right end. Now, substitute the value of the octal number into it.
What is the formula to convert a decimal number into a binary number?
A decimal number can be converted into a binary number by dividing the given number by 2 continuously till we get the quotient as 1 and write the numbers from downwards to upwards.
Binary Formula
Binary formulas are formulas that are used to convert binary numbers to other number systems. A binary number system is a system of numbers that has a base of 2 and uses only two digits, “0 and 1”. It is one of the four types of number systems and is most commonly employed by computer languages like Java and C++. “Bi” in the word “binary” stands for “two.” Some examples of binary numbers are (11)2, (1110)2, (10101)2, and so on.
In this article, we discuss the arithmetic operations of binary numbers and the conversion formulae to convert binary numbers into other three-number systems.
Table of Content
- Binary Formula
- Arithmetic Operation on Binary Numbers
- Binary to Decimal Formula
- Decimal to Binary Formula
- Binary to Octal Formula
- Binary to Hexadecimal Formula
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