Binary to Decimal Conversion

There are several traditional methods of converting the numbers from binary to decimal conversion. We shall discuss here the two most commonly used methods, namely; “Expansion method and Value Box method”.

(i) Expansion Method:

In this method, the given number is expressed as a summation of terms each of which is the product of a bit (0 or 1) and a power of 2. The power of 2 is determined from the bit position.

Thus the decimal equivalent of a binary number has the general form;

a_n-1 a_n-2 …. a_i ….. a₁ ….. a₀ ∙ a_-1 a_-2 ….. a_-p

= a_n-1 × 2^n-1 + a_n-2 x 2^n-2 + ….. +a_i x 2ⁱ + …. + a₁ x 2¹ + a₀ x 2⁰ + a_-1 x 2^-1 + a_-2 x 2^-2 + …. + a_-p x 2^-p

(ii) Multiplication and Division Method:

The value box method of converting numbers from decimal to binary is laborious and time consuming and is suitable for small numbers when it can be performed mentally. It is advisable not to use it for large numbers. The conversion of large numbers may be conveniently done by multiplication and division method which is described below.

To effect the conversion of positive integers of the decimal system to binary numbers the decimal number is repeatedly divided by the base of the binary number system, i.e., by 2. The division is to be carried until the quotient is zero and the remainder of each division is recorded on the right. The binary equivalent of the decimal number is then obtained by writing down the successive remainders. The first remainder is the least significant bit and the last one is the most significant bit of the binary number. Thus the binary equivalent is written from the bottom upwards.

● Binary Numbers