Decimal Number System

Number system with base value 10 is termed as Decimal number system. It uses 10 digits i.e. 0-9 for the creation of numbers. Here, each digit in the number is at a specific place with place value a product of different powers of 10. Here, the place value is termed from right to left as first place value called units, second to the left as Tens, so on Hundreds, Thousands, etc. Here, units has the place value as 10⁰, tens has the place value as 10¹, hundreds as 10², thousands as 10³, and so on. 

Conversion from Binary Number System to Other Number Systems

Binary Numbers are represented with digits 0 and 1 and with base 2. Conversion of a number system means conversion from one base to another. Following are the conversion of the Binary Number System to other Number Systems:

Steps for Conversion of Binary to Decimal Number System

Binary numbers are represented in base 2 but the decimal numbers are of base 10. Hence, to convert the binary number into a decimal number, the base of that number is to be changed. Follow the steps given below:

• Step 1: Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base.
• Step 2: The exponents should start with 0 and increase by 1 every time we move from right to left.
• Step 3: Simplify each of the above products and add them.

Example: To convert (11101011)₂ into a decimal number

Steps for Conversion of Binary to Octal Conversion:

Binary numbers are represented in base 2 but the octal numbers are of base 8. Hence, to convert the binary number into octal number, the base of that number is to be changed. Follow the steps given below:

• Step 1: Divide the binary number into groups of three digits starting from right to left i.e. from LSB to MSB.
• Step 2: Convert these groups into equivalent octal digits.

Example: To convert (11101011)₂ into an octal number

Steps for Conversion of Binary to Hexadecimal Conversion:

Binary numbers are represented in base 2 but the Hexadecimal numbers are of base 10. Hence, to convert the binary number into Hex number, the base of that number is to be changed. Follow the steps given below:

• Step 1: Divide the binary number into groups of four digits starting from right to left i.e. from LSB to MSB.
• Step 2: Convert these groups into equivalent hex digits.

Example: To convert (1110101101101)₂ into a hex number