Learning About Binary to Decimal Conversion

Learning About Binary to Decimal Conversion

Binary to Decimal

All number systems are known to have a base that represents the number of digits that are used in that number system. The binary number system uses two digits (0 and 1) to denote a number so its base value is 2. The numbers in the binary system are represented as a combination of these two digits only. Digits 0 and 1 are bits. This number system is used in computers for data handling as the computer systems use data in binary form. Binary to Decimal is an important conversion that you should know. Again, the decimal number system uses ten digits (0 to 9) to represent a number, so it has a base value of 10. The decimal number system is the most commonly use method to represent numbers in everyday life.

If you take a binary number, say (101101)2

  1. The first step is to mention the empower of 2 beginning from the extreme right. The first one will be 2 0 and the last one would be 25.
  2. Multiply it with its numbers. 1* 20 + 0* 21 + 1 * 22 + 1 * 23 + 0*24 + 0*25 = 45
  3. (10110 1)2 = (45)10

A binary number can be represent in the corresponding decimal number form. It is the conversion of a given number in a binary number system to its equivalent number in the decimal number system. The conversion of numbers from binary to decimal is required to read binary numbers conveniently in a decimal format. The decimal number system uses any of the 10 digits (0 to 9) to represent a number. So it has a base of 10. The binary number system represents a number using only two digits, 0 and 1. For conversion of a binary number to a decimal number is done by two methods as mention below: 

Positional Notation Method

In this method of conversion, the value of a digit in a binary number is obtain on its position. In this process, we multiply each digit of the number by 2 to the power that corresponds to the place of that digit in the number. The values thus calculated for each digit are add to get the decimal number equivalent to the given binary number. It is to be note for a binary number with ‘n’ digits, the rightmost digit has a weight of 2 raised to the power of 0 and the leftmost digit has a value of 2 raised to the power of n-1.

Doubling Method

In this method, starting from the left-most digit of the given binary number, we double the previous digit and add the value with the current digit. For the leftmost digit, zero is add . This same process is continue one by one for all the digits of the binary number. A binary number can be represent in the corresponding decimal number form. It is the conversion of a given number in a binary number system to its equivalent number in the decimal number system. The decimal number system uses any of the 10 digits (0 to 9) to represent a number. So it has a base of 10.

The sum of all the values finally achieved is the decimal number equivalent of that binary number. Learn the concept in detail from cuemath.com. All number systems are  base that represents . The number of digits that are use in that number system. The binary number system uses two digits (0 and 1) to denote a number so its base value is 2. The numbers in the binary system are represent as a combination of these two digits only. Digits 0 and 1 are call bits. This number system is use in computers for data handling as the computer systems use data in binary form.

Is Converting Binary to Decimal Easy?

The decimal number system uses any of the 10 digits (0 to 9) to represent a number. So it has a base of 10. The binary number system represents a number using only two digits, 0 and 1. Therefore this number system is  to have a base of 2. A decimal number can be representx as an equivalent binary number. When a decimal number is convert to an equivalent binary number, the base of the number changes from 10 to 2. This is how decimal to binary conversion takes place.

 The commonly used method for converting a decimal number into a binary number is by performing short division by 2 with the remainder (for integer part) and performing short multiplication by 2 with the result (for the decimal part). Digits 0 and 1 also known as bits. This number system is use in computers for data handling as the computer systems use data in binary form. Binary to Decima l is an important conversion that you should know. Again, the decimal number system uses ten digits (0 to 9) to represent a number, so it has a base value of 10. The decimal number system is the most commonly use method to represent numbers in everyday life.

Binary to Decimal Conclusion

 To convert a decimal number to a binary number, the integer part of a given decimal number is divided by 2 repeatedly. The remainder in each step is note down till 0 is obtain as the final quotient. These remainders, when written in reverse order, give the binary value of the integer part of the given decimal number.A binary number can be represent in the corresponding decimal number form. It is the conversion of a given number in a binary number system to its equivalent number in the decimal number system. 

 For conversion of a decimal part of the number to an equivalent binary value, multiply it by 2. Note down the value of the integer part of the product, which will be 0 or 1. Continue multiplying the remaining decimal part . And note the integer part of the result of every step till we get 0. Then write the note integer values serially. Which will be the equivalent binary number of the given decimal part.

Written by
Rex Baker