Decimal to Binary

Various methods are used to convert decimal to binary. Divide the provided decimal number recursively by 2 is one way for converting decimal to binary. The remainders are then recorded until the final quotient is zero. These remainders are then rewritten in reverse order to obtain the binary value of the provided decimal number. A number system is a method of expressing numbers mathematically with a set of digits or symbols. The decimal number system, binary number system, octal number system, and hexadecimal number system are examples of distinct number systems.

Decimal to Binary Conversion

Various methods are used to convert decimal to binary. Every number system has a base that is determined by the total number of digits in the system. The binary number system, for example, has a base of two since it only utilises two digits to express a number. Similarly, because each number is represented by ten digits, the decimal number system has a base of ten.. Let’s start by learning about the decimal and binary number systems, and then we’ll look at how to convert decimal to binary.

Decimal Number System Definition

Numbers with a base of ten are represented by ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It’s also known as the Hindu-Arabic number system, in which each digit has a location and is 10 times more important than the one before it. A decimal point is also used to denote decimal fractions. For example, in the decimal number 36, 3 is 10 times more than 6. 4510, 11810, and so on are examples of decimal numerals. It is the most widely used number system, with numbers that can be easily recognised even if the base is not printed.

Binary Number System Definition

Binary numbers are a base-2 number system, in which numbers can only be represented by two digits: 0 and 1. A bit is the shortened version of ‘binary digit,’ which is the smallest unit of data in a computer. A bit has just one binary value: either 1 or 0. Binary numbers are expressed as 1102, 102 and are commonly used in computers for programming or coding since computers only comprehend binary digits, i.e. 0 and 1.

Decimal to Binary Table

Converting numbers from decimal to binary can be done in a variety of ways. The basis of a number changes from 10 to 2 when it is converted from decimal to binary. It’s worth noting that every decimal number has a binary counterpart. The decimal to binary chart of the first 20 whole numbers is shown in the table below.

Decimal NumbersBinary Numbers
00
11
210
311
4100
5101
6110
7111
81000
91001
101010
111011
121100
131101
141110
151111
1610000
1710001
1810010
1910011
2010100

How to Convert Decimal to Binary?

To convert numbers from decimal to binary, multiply the provided decimal value by 2 and record the remainders until the final quotient is zero. The following stages are the decimal to binary formula, which demonstrates the conversion process.

  • Step 1: Take the remaining after dividing the supplied decimal value by two.
  • Step 2: Multiply the obtained quotient by two and record the residual.
  • Step 3: Repeat the previous steps until the quotient is zero.
  • Step 4: Now write the remainders in the opposite sequence, with the latest remainder written first.
  • Step 5: Another way to think about it is that the binary number’s Least Significant Bit (LSB) is at the top and the Most Significant Bit (MSB) is at the bottom. The binary value of the given decimal number is this number.

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