Decimal to binary conversion
Converts a decimal number into binary format.
The decimal (base ten) numeral system has ten possible values (0,1,2,3,4,5,6,7,8, or 9) for each place-value. In contrast, the binary (base two) numeral system has two possible values represented as 0 or 1 for each place-value.[1] Since the binary system is the internal language of electronic computers, serious computer programmers should understand how to convert from 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.
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.
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.
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.