a (n-1) and a n are integer part digits, n is the total number of integer digits. Representing real number in base-r is as following below −Ī nxr n+a (n-1)xr (n-1)+. The coefficient a j ranges from 0 to (r-1). In general, a number expressed in base-r system has coefficients multiplied by power of r. Here, right most bit 6 is the least significant bit (LSB) and left most bit 2 is the most significant bit (MSB). Each position in the decimal system is 10 times more significant than the previous position, that means numeric value of a decimal number is determined by multiplying each digit of the number by the value of the position in which the digit appears and then adding the products.Įxample-1 − The number 2025 is interpreted as − 2025 = 2x10 3+0x10x 2+2x10x 1+5x10 0 = 2000+0+20+5 = 2005 Position of every digit has a weight which is a power of 10. This is also known as base-10 number system which has 10 symbols, these are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. This is the weighted (or positional) number representation, where value of each digit is determined by its position (or their weight) in a number. If the Base value of a number system is 10, then it is called Decimal number system which has most important role in the development of science and technology. For example, Binary, Octal, Decimal and Hexadecimal Number systems are used in microprocessor programming. Based on its Base value, a number has unique representation and different number systems have different representation of the same number.
Number System represents value of number with respect to its given base.
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