Solved Examples on Binary Formula
Example 1: Convert the decimal number (73)10 into binary.
Solution:
To convert the (73)10 into a binary number, we have to divide it continuously by 2 until we obtain the quotient of 1.
Thus, (73)10 in the binary number system is (1001001)2.
Example 2: Convert the binary number (110010101)2 to octal.
Solution:
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.
110010101 ⇒ 110 – 010 – 101
6 – 2 – 5 = 625
Therefore, the binary number (110010101)2 in the octal system is 625.
Example 3: Convert the binary number (10110110)2 to hexadecimal.
Solution:
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.
10110110 ⇒ 1011 – 0110
(1011)2 = (B)16
(0110)2 = (6)16
So, (10110110)2 = (B6)16
Therefore, the binary number (10110110)2 in the hexadecimal system is B6.
Example 4: Add (1011010)2 and (1101011)2.
Solution:
Hence, (1011010)2 + (1011010)2 = (1000101)2.
Example 5: Multiply (110)2 and (101)2.
Solution:
Thus, (110)2 × (101)2 = (11110)2.
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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