Decimal to Binary

Decimal to binary conversion is done through various methods. One of the methods to convert decimal to binary is by dividing the given decimal number recursively by 2. Then, the remainders are noted down till we get 0 as the final quotient. After this step, these remainders are written in reverse order to get the binary value of the given decimal number. A number system is a mathematical way of representing numbers using a set of digits or symbols. There are different number systems like the decimal number system, the binary number system, the octal, and the hexadecimal number system. These are identified with the help of the base that they have. Numbers can be easily converted from one base to another using some defined rules.

Decimal to binary conversion means when we convert a number from the decimal number system to the binary number system. All number systems have a base which is determined by the total number of digits that are used in the number system. For example, the binary number system has a base of 2 since it uses only two digits to represent a number. Similarly, the decimal number system has a base of 10, because it has 10 digits to represent a number. Let us understand the decimal number system and the binary number system and then move on to the conversion of decimal to binary.

Decimal Number System Definition

The decimal number system is a number system that represents a number with a base of 10 and uses 10 symbols - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is also known as the Hindu-Arabic number system in which each digit has a position and it is ten times more significant than the previous digit. It also uses a decimal point to represent decimal fractions. For example, if we take 36 as a decimal number, here, 3 is ten times more than 6. Decimal numbers are written as 45₁₀, 118₁₀, and so on. It is the most commonly known number system in which the numbers can be identified easily even if the base is not written. In other words, if the base of a number is not written, it is considered to be a decimal number.

Binary Number System Definition

The binary number system is a number system with base 2 in which numbers are represented only by two digits, 0 and 1. The smallest unit of data in a computer is called a bit, which is the abbreviated form of 'binary digit'. A bit has a single binary value which is either 1 or 0. Binary numbers are written as 110₂, 10₂ and are mostly used in computers for programming or coding since the computer understands the language of only the binary digits, that is, 0 and 1. It should be noted that in a binary number, the bit to the extreme left is called the Most Significant Bit (MSB), and the bit to the extreme right end is known as the Least Significant Bit (LSB). The remaining part shows the magnitude of the number.

To convert numbers from decimal to binary, the given decimal number is divided repeatedly by 2 and the remainders are noted down till we get 0 as the final quotient. The following steps is considered as the decimal to binary formula that shows the procedure of conversion.

• Step 1: Divide the given decimal number by 2 and note down the remainder.
• Step 2: Now, divide the obtained quotient by 2, and note the remainder again.
• Step 3: Repeat the above steps until you get 0 as the quotient.
• Step 4: Now, write the remainders in such a way that the last remainder is written first, followed by the rest in the reverse order.
• Step 5: This can also be understood in another way which states that the Least Significant Bit (LSB) of the binary number is at the top and the Most Significant Bit (MSB) is at the bottom. This number is the binary value of the given decimal number.

Let us understand this with an example.

Example: Convert the decimal number 13₁₀ to binary.

Solution: We will start dividing the given number (13) repeatedly by 2 until we get the quotient as 0. We will note the remainders in order.

After noting the remainders, we will write them in such a way that the Most Significant Bit (MSB) of the binary number is written first, followed by the rest. Therefore, the binary equivalent for the given decimal number 13₁₀ is 1101₂. This means that 13₁₀ = 1101₂.

There are different methods of converting numbers from decimal to binary. When we convert numbers from decimal to binary, the base of the number changes from 10 to 2. It should be noted that all decimal numbers have their equivalent binary numbers. The following table shows the decimal to binary chart of the first 20 whole numbers.

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What are the Rules to Convert Decimal to Binary?

The rules to convert decimal to binary numbers are given below:

• Write down the number.
• Divide it by 2 and note the remainder.
• Divide the quotient obtained by 2 and note the remainder.
• Repeat the same process till we get 0 as the quotient.
• Write the values of all the remainders starting from the bottom to the top. That will be the required answer.

What is the Purpose of Converting Numbers from Decimal to Binary?

Binary numbers are used for programming and coding in computers. Since a computer understands the language of binary digits, 0 and 1, numbers are converted from decimal to binary. When we do decimal to binary conversions, the base of the decimal numbers changes from 10 to 2.

What Does the Decimal to Binary Table Show?

The decimal to binary table is a conversion chart that shows all decimal numbers along with their equivalent binary numbers. For example, it shows that the binary value of 0 is 0, the binary value of 1 is 1, the binary value of 2 is 10, the binary value of 3 is 11, and so on.

How is the Decimal to Binary Conversion Done?

The simplest way to convert a decimal number to a binary number is by dividing the given number repeatedly by 2 until we get 0 as the quotient. Then, we write the remainders in the reverse order to get the binary value of the given decimal number.

What is the Decimal 254 in Binary?

The decimal number 254 is equal to 11111110 in binary, that is, 254₁₀ = 11111110₂.

List the Decimal to Binary Values of the First Ten Decimal Numbers.

The following list shows the first ten decimal numbers along with the corresponding binary equivalents.

• 0 - 0
• 1 - 1
• 2 - 10
• 3 - 11
• 4 - 100
• 5 - 101
• 6 - 110
• 7 - 111
• 8 - 1000
• 9 - 1001
• 10 - 1010

What is the Binary Equivalent of the Decimal Value 97?

The binary equivalent of 97 is 1100001. This can be written as 97₁₀ = 1100001₂ which shows that 97 with base 10 is converted to 1100001 of base 2.

What is the Decimal to Binary Formula?

The decimal to binary formula is used by performing division on the given decimal number recursively by 2 and noting down the remainders till we have either 0 or 1 as the final quotient. The steps that are used to convert numbers from decimal to binary number are shown below.

• Step 1: Divide the given decimal number by 2 and note down the remainder.
• Step 2: Now divide the quotient thus obtained in the above step by 2 and note down the remainder.
• Step 3: Repeat the above steps until we get 0 or 1 as a quotient.
• Step 4: Write down the values of all the remainders from the bottom to the top. This gives the binary conversion of the given decimal number.

How to Convert a Number to Binary?

When we say that we need to convert a number to binary, we mean that a decimal number needs to be converted to a binary number. Let us understand this with the help of an example using the following method. Let us convert 5 to binary.

• Step 1: Divide 5 by 2 and note the remainder. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.
• Step 2: Write the remainder in reverse chronological order, from the bottom to the top. This will give the binary equivalent of the number 5.
• Step 3: After its procedure, the binary equivalent of the number 5 is obtained as 101.