Repeat the same process till we get 0 as the quotient. Divide the quotient obtained by 2 and note the remainder. The rules to convert decimal to binary numbers are given below: This means that 13 10 = 1101 2.įAQs on Decimal to Binary What are the Rules to Convert Decimal to Binary? Therefore, the binary equivalent for the given decimal number 13 10 is 1101 2. We will note the remainders in order.Īfter 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. Solution: We will start dividing the given number (13) repeatedly by 2 until we get the quotient as 0. This number is the binary value of the given decimal number.Įxample: Convert the decimal number 13 10 to binary. 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. 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 3: Repeat the above steps until you get 0 as the quotient. Step 2: Now, divide the obtained quotient by 2, and note the remainder again. Step 1: Divide the given decimal number by 2 and note down the remainder. The following steps is considered as the decimal to binary formula that shows the procedure of conversion. 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 remaining part shows the magnitude of the number. 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). Binary numbers are written as 110 2, 10 2 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. A bit has a single binary value which is either 1 or 0. The smallest unit of data in a computer is called a bit, which is the abbreviated form of 'binary digit'. The binary number system is a number system with base 2 in which numbers are represented only by two digits, 0 and 1. In other words, if the base of a number is not written, it is considered to be a decimal number. 
It is the most commonly known number system in which the numbers can be identified easily even if the base is not written. Decimal numbers are written as 45 10, 118 10, and so on. For example, if we take 36 as a decimal number, here, 3 is ten times more than 6. It also uses a decimal point to represent decimal fractions. 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. 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. Let us understand the decimal number system and the binary number system and then move on to the conversion of decimal to binary. Similarly, the decimal number system has a base of 10, because it has 10 digits to represent a number. For example, the binary number system has a base of 2 since it uses only two digits to represent a number. Now, join both the result 15.125 (decimal) = 1111.All number systems have a base which is determined by the total number of digits that are used in the number system. 'Integer' column in table 2 occurs from the integer part of 'Result' column of table 2. Note: Read the Integer from top to bottom.Įxplanation: Here, you have to stop the table when no more fractional part is available in 'Result' column of table 2. Now, convert the Fraction part of the given decimal number (0.125) into a binary number.
Note: Read the remainder from bottom to top. Now, convert the Integer part of the given decimal number (15) into a binary number. Here, we have to split the fractional decimal number into two parts. In this example, we will convert the fractional decimal number ( 15.125) to a binary number ( 1111.001).
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