Science

Definition of number system:- Numbering systems are based on the "maximum" value of a single digit. IN day to day life we use the decimal system 0 to 9. The heart of the computer is binary (0,1), there was a ternary computer (0, 1, 2), octal (0-7) and hexadecimal . Hexadecimal is essentially 1 to 15 but since you only have a single digit to express on unit then alpha characters had to be used so hexadecimal is 0-9, A-F where A = 10 and F = 15

Number Systems, Base Conversions, and Computer Data Representation Decimal Number When we write decimal (base 10) numbers, we use a positional notation system. Each digit is multiplied by an appropriate power of 10 depending on its position in the number: For example:

843 = 8 x +4× = 800 + 40 + 3

+3×

However, decimal number’s base is 10. So, 843 is written as (843) For whole numbers, the rightmost digit position is the one’s position (10 = 1). The numeral in that position indicates how many ones are present in the number. The next position to the left is ten’s, then hundred’s, thousand’s, and so on. Each digit

position has a weight that is ten times the weight of the position to its right. In the decimal number system, there are ten possible values that can appear in each digit position, and so there are ten numerals required to represent the quantity in each digit position. The decimal numerals are the familiar zero through nine (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Binary number:- Generally, the radix will be understood from the context and the radix specification is left off. The binary number system is also a positional notation numbering system, but in this case, the base is not ten, but is instead two. Each digit position in a binary number represents a power of two. So, when we write a binary number, each binary digit is multiplied by an appropriate power of 2 based on the position in the number: For example: 101101 = 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 1 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 0 x 2...