This is recorded as second binary digit and this process will go on till the quotient becomes 0. The reminder is recorded as first binary digit and the quotient is again divided by the base number, thus we get second quotient and second reminder. When the decimal number is divided with its base number, we get a quotient called “R eminder”. The method of converting whole numbers from one base to another is known as “ Repeated division”. They are 1.Multiplying Each Binary Number by its Position ValueĬounting from right, the value of the right most bit is 1, value of next bit is 2, value of next bit is 4 and value of next bit is 8 and so on.įor example, convert 1011 to decimal numberĪ well known and easy method for converting decimal numbers into binary numbers is “Repeated division by 2”. We can convert a binary number to decimal number by 2 ways. In general we will measure the size of memory in Bytes. The data to the computer, must be in the form of binary digits 0’s & 1’s.Įxamples for understanding the binary number systemĢ1 is expressed in binary system as 10101 2 = 1 × 2 4 + 0 × 2 3 + 1 × 2 2 + 0 ×2 1 + 1 ×2 0 = 16 + 4 + 1 = 21Ģ3 is expressed in binary system as 10111 2 = 1 × 2 4 + 0 × 2 3 + 1 × 2 2 + 1 × 2 1 + 1 × 2 0 = 16 + 4 + 2 + 1 = 23ģ5 is expressed in binary system as 100011 2 = 1 × 2 5 + 0 × 2 4 + 0 × 2 3 + 0 × 2 2 + 1 × 2 1 + 1 × 2 0 = 32 + 2 + 1 = 35Ġ or 1 is called as ‘ BIT’.‘ NIBBLE’ is a combination of 4 bits. Mostly binary system is used in digital systems. It is a positional number system this means the positions are weighted as the powers of 2. The binary number system uses only two digits 0 & 1. In power of 10 we can write the above number asĥ x 10 3 + 6 x 10 2 + 7 x 10 1 + 8 x 10 0 + 9 x 10 -1 Here the left most bit is called “Most significant bit” or “ MSB” and the right most bit is called “Least significant bit” or “LSB”.

Let us calculate a number in decimal system as follows.Ĩ48: Eight hundred and forty eight.

The position of a digit with reference to the decimal point determines its value. In this system, we consider the positions of digits in a number as units, tens, hundreds, thousands & etc. This is the number system which we are using in our daily life. 1.Multiplying Each Binary Number by its Position Value.Examples for understanding the binary number system.

Binary to decimal conversion table