**Q. Define Number Systems?**

A number system, in general, is an ordered set of symbols (digits) with relationships defined for addition, subtraction, multiplication, and division. The base (radix) of the number system is the total number of digits in the system. For example, in our decimal system, the set of digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and hence the base (radix) is ten (10); in the binary system, the set of digits (bits) is {0, 1} and hence the base or radix is two (2).

There are two possible ways of writing a number in a given system: positional notation and polynomial representation. For example, the number 2536.47 in our decimal systemis represented in positional notation as (2536.47)10, whereas in polynomial form it is 2 × 10^{3} + 5 × 10^{2} + 3 ×

101 + 6×100 + 4×10^{-1}+ 7×10^{-2}. The radix or base is 10, whereas the most significant digit or bit (MSB) is 2, the least significant digit or bit (LSB) is 7; the number of integer bits (digits) is 4, and the number of fractional bits (digits) is 2.