Number systems

The left-most bit

The most significant bit in the binary system.

Unsigned number

A non-negative integer; where all the bits contribute to magnitude

Signed number

A number that can be positive or negative.

The left most bits is a sign; 1 is negative and 0 is positive. And rest of the bits are magnitude.

Positional (radix-r) representation

A system where the value of a number is expressed as a weighted sum of digits, each digit multiplied by a power of the radix r.

V = Σki*r^i

General formula for positional (radix-r) representation

The radix r which is associated with the i digit’s position is what determines the weight of each digit.

V

Symbol that represents the value of number being represented inside the general formula for positional (radix-r) representation

Σ

Symbol that represents the summation (we add up all the terms across the digit positions) in the general formula for positional (radix-r) representation

ki

Symbol that represents the digit at the position i inside the general formula for positional (radix-r) representation

r

Symbol that represents the radix of the number, which is also called the base number.

i

Symbol that represents the position index which can be positive for the integer places and negative for the fractional places. It is raised by the radix symbol

10: (0-9)

Radix of the decimal

2: (0-1)

Radix of the binary

8: (0-7)

Radix of the octal

16: (0-9; A-F)

Radix of the hexadecimal

Group bit in 3s from the LSB

Binary → Octal conversion rule

Group bits in 4s from the LSB

Binary → Hexadecimal conversion rule