Binary Formula
Binary Formula- A binary number system is a set of numbers with a base of two and just two digits, “0 and 1”. It is one of the four types of number systems and is most widely used in programming languages such as Java and C++. “Bi” in the term “binary” means “two.” Examples of binary numerals include (11)2, (1110)2, (10101), and so on. The radix of a binary integer is 2, and each digit is referred to as a bit. A binary number may be transformed into three different number systems: decimal, octal, and hexadecimal. In this article, we explore the arithmetic operations on binary numbers and the conversion equations that transform binary numbers into other three number systems.
Binary Formula
To grasp the binary number system, we must first appreciate how it works. Binary numbers are widely employed in electrical circuits that produce logic gates, as well as by microcontrollers for logical computing. A binary number has only two digits, “0 and 1,” and each digit is known as a bit. The computer’s input is initially translated to binary using an assigned ASCII code. Furthermore, the information is transformed from binary to user language and shown as an output.
Arithmetic Operation on Binary Numbers
Binary Addition
Binary number addition differs from regular addition, yet it is still quite straightforward. To add two binary integers, we must do it digit by digit. The sum of two binary integers is a binary number. To further comprehend binary number addition, refer to the table below.
|
Binary number 1 |
Binary number 2 |
Sum |
Carry |
|---|---|---|---|
|
0 |
0 |
0 |
0 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
1 |
Binary Subtraction
Binary number addition differs from regular addition, yet it is still relatively simple. To add two binary integers, we must do it digit by digit. The sum of two binary integers is a binary number. To further comprehend binary number addition, refer to the table below.
|
Binary number 1 |
Binary number 2 |
Difference |
Borrow |
|---|---|---|---|
|
0 |
0 |
0 |
0 |
|
0 |
1 |
1 |
1 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
0 |
Binary Multiplication
Binary multiplication is similar to the multiplication of normal numbers. Have a look at the table given below to understand the multiplication of binary numbers.
|
Binary number 1 |
Binary number 2 |
Multiplication |
|---|---|---|
|
0 |
0 |
0 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
Binary to Decimal Formula
A binary number’s decimal equivalent is determined by performing a binary-to-decimal conversion on the Binary Formula. A number system is a format that specifies how to represent numbers. The binary number system, which only has the digits 0 and 1, is used in computers and other electronic devices to represent data. The most widely used and most widely understood number system in the world is the decimal system. The positional notation approach and the doubling method are two ways to convert from binary to decimal.
|
Decimal Number |
Binary number |
Decimal Number |
Binary number |
|---|---|---|---|
| 1 | 001 | 11 | 1011 |
| 2 | 010 | 12 | 1100 |
| 3 | 011 | 13 | 1101 |
| 4 | 100 | 14 | 1110 |
| 5 | 101 | 15 | 1111 |
| 6 | 110 | 16 | 10000 |
| 7 | 111 | 17 | 10001 |
| 8 | 1000 | 18 | 10010 |
| 9 | 1001 | 19 | 10011 |
| 10 | 1010 | 20 | 10100 |
Decimal to Binary Formula
The formula for converting decimal values to binary numbers is known as the “decimal-to-binary conversion.” The remainder formula makes it simple to translate decimal integers into binary numbers. The technique involves repeatedly dividing the provided decimal value by 2 and noting the remainder until we arrive at a quotient of 0 or 1. The given decimal number will be divided recursively by two in the formula to convert decimal to binary, and the remainder will be noted until we have either 0 or 1 as the final quotient.
A digit in a number is given a weight based on its position when using the positional notation method. To accomplish this, multiply each digit by the base (2) increased to the appropriate power, depending on where that digit falls in the number. The equivalent value of the supplied binary number in the decimal system is determined by adding up all of these values received for each digit.
Binary to Octal Formula
In contrast to the decimal number system, the binary and octal number systems use distinct conventions to write numbers. The only digits used to represent numbers in the Binary Formula system are 0 and 1, but 0 to 7 digits are used to represent numbers in the octal number system. By applying a set of principles, any number that is written using one number system can be translated into another.
|
Binary number |
Octal Number |
Binary number |
Octal Number |
|---|---|---|---|
| 000 | 0 | 1000 | 10 |
| 001 | 1 | 1001 | 11 |
| 010 | 2 | 1010 | 12 |
| 011 | 3 | 1011 | 13 |
| 100 | 4 | 1100 | 14 |
| 101 | 5 | 1101 | 15 |
| 110 | 6 | 1110 | 16 |
| 111 | 7 | 1111 | 17 |
Binary to Hexadecimal Formula
Another conversion that takes place in the number system is from Binary Formula to hexadecimal. In mathematics, there are four different sorts of number systems: binary, octal, decimal, and hexadecimal. These forms can all be converted using the conversion method or conversion table to the other type of number system.
The process of translating binary numbers into hexadecimal values is known as “binary-to-hexadecimal conversion.” Hexadecimal has a base number of 16, whereas binary digits have a base number of 2. With the help of the base numbers, binary is converted to hexadecimal. There are several ways to perform the conversion; the first is by changing the binary representation into a decimal number and then a hexadecimal number.
|
Decimal number |
Binary number |
Hexadecimal Number |
Decimal number |
Binary number |
Hexadecimal number |
|---|---|---|---|---|---|
| 0 | 0000 | 0 | 8 | 1000 | 8 |
| 1 | 0001 | 1 | 9 | 1001 | 9 |
| 2 | 0010 | 2 | 10 | 1010 |
A |
| 3 | 0011 | 3 | 11 | 1011 |
B |
| 4 | 0100 | 4 | 12 | 1100 |
C |
| 5 | 0101 | 5 | 13 | 1101 |
D |
| 6 | 0110 | 6 | 14 | 1110 |
E |
| 7 | 0111 | 7 | 15 | 1111 |
F |
Solved Examples on Binary Formula
Example 1: Convert the binary number (110010100)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 – 100
6 – 2 – 4 = 624
Therefore, the binary number (110010100)2 in the octal system is 624.
Example 2: Convert the binary number (10010111)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.
10010111 ⇒ 1001 – 0111
(1001)2 = (9)16
(0111)2 = (7)16
So, (10010111)2 = (97)16
Therefore, the binary number (10010111)2 in the hexadecimal system is 97.
FAQs (Frequently Asked Questions)
1. What does Binary to Hexadecimal mean?
A Binary Formula with a base of 2 is converted to a hexadecimal number with a base of 16 in the process known as “binary to hexadecimal.” Only 2 integers, or bits, make up binary numbers: 0 and 1. Hexadecimal numerals, which range from 0 to 9, and A to F, only deal with numbers (10–15).
2. What in Binary Does the Hexadecimal Number F Equal?
F Equals 1111, according to the binary-to-hexadecimal conversion chart.
3. What is the process by which a binary number is transformed into an octal number?
We can convert a Binary Formula into an octal number using one of two methods: either straight from binary to octal, or from binary to decimal, and then from the resulting decimal back to binary. We must first divide the given binary number into two groups of three digits, starting at the right end, to convert it from binary to octal. Now, replace it with the octal number’s value.
