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*103
- 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 ô 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 ô 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 ô 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.
- Step 5 – Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3. ó
- 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.
