A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

The value of each digit in a number can be determined using −

- The digit
- The position of the digit in the number
- The base of the number system (where the base is defined as the total number of digits available in the number system)

- Binary number system
- Octal number system
- Decimal number system
- Hexadecimal (hex) number system

- The number system that we use in our day-to-day life is the decimal number system. The decimal number system has a base of 10 as it uses 10 digits from 0 to 9. In the decimal number system, the successive positions to the left of the decimal point represent units, tens, hundreds, thousands, and so on.
- This computer understands everything in the multiple of 10.
- Like 721, seven in the first position of a three-digit number. So it will translate 7*10
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- Characteristics of the binary number system are as follows −
- Uses two digits, 0 and 1
- Also called a base 2 number system
- Each position in a binary number represents a 0 power of the base (2). Example 20
- The last position in a binary number represents the x power of the base (2). Example 2x where x represents the last position – 1.

- Characteristics of the octal number system are as follows −
- Uses eight digits, 0,1,2,3,4,5,6,7
- Also called a base 8 number system
- Each position in an octal number represents a 0 power of the base (8). Example 80
- The last position in an octal number represents the x power of the base (8). Example 8x where x represents the last position – 1

- Characteristics of hexadecimal number system are as follows −
- Uses 10 digits and 6 letters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
- Letters represent the numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15
- Also called as base 16 number system
- Each position in a hexadecimal number represents a 0 power of the base (16). Example, 160
- Last position in a hexadecimal number represents a x power of the base (16). Example 16x where x represents the last position – 1

**Step 1 −** Divide the decimal number to be converted by the value of the new base.

**Step 2 −** Get the remainder from Step 1 as the rightmost digit (least significant digit) of the new base number.

**Step 3 − **Divide the quotient of the previous divide by the new base.

**Step 4 −** Record the remainder from Step 3 as the next digit (to the left) of the new base number.

**Repeat Steps 3 and 4**, getting remainders from right to left, until the quotient becomes zero in Step 3. •

The last remainder thus obtained will be the Most Significant Digit (MSD) of the new base number.

**Step 1** − Convert the original number to a decimal number (base 10).

**Step 2** − Convert the decimal number so obtained to the new base number.