Representation of Numbers

Every digital computer uses the binary number system for data representation, composed of just two digits, 0 and 1.
In contrast, humans normally use the decimal number system, which includes ten digits (0 to 9).
The binary system is based on powers of 2. For example, from right to left, 2^0, 2^1, 2^2 and so forth.
Changing a decimal number to binary involves dividing the decimal number by 2 and noting down the remainder until the dividend equals zero. The binary equivalent is the reverse of the noted remainders.

The hexadecimal system includes 16 symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen.
Hexadecimal numbers are useful in computing because they can represent every byte (8 bits) as two consecutive hexadecimal digits, thus providing a more human-friendly representation of binary-coded values.

Two’s complement is a method for representing signed integers (positive or negative) in binary.
To obtain the two’s complement of a binary number, first invert all the bits (0 to 1 and 1 to 0), then add 1 to the result.
The leftmost bit of a twos-complement number is the sign bit. If the sign bit is 1, the number is negative; if it’s 0, the number is positive.

Floating point representation is a way to approximate real numbers in binary, where a number is represented by two main parts: the significand (or mantissa) and the exponent.
The mantissa provides precision, while the exponent expands the range of values that can be represented.
This is similar to scientific notation in decimals. For example, the number 300 can be represented as 3 x 10^2 in scientific notation.
Floating point representation allows computers to handle very large numbers or extremely small fractions.