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;

an-1 an-2 …. ai ….. a1 ….. a0 ∙ a-1 a-2 ….. a-p

= an-1 × 2n-1 + an-2 x 2n-2 + ….. +ai 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

  • Why Binary Numbers are Used
  • Binary to Decimal Conversion
  • Conversion of Numbers
  • Hexa-decimal Number System
  • Conversion of Binary Numbers to Octal or Hexa-decimal Numbers
  • Octal and Hexa-Decimal Numbers
  • Signed-magnitude Representation
  • Radix Complement
  • Diminished Radix Complement
  • Arithmetic Operations of Binary Numbers

From Binary to Decimal Conversion to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  2. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    Read More

  3. Tenths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 12:03 PM

    Tenth Place in Decimals
    The first place after the decimal point is tenths place which represents how many tenths are there in a number. Let us take a plane sheet which represents one whole. Now, divide the sheet into ten equ…

    Read More

  4. Representing Decimals on Number Line | Concept on Formation of Decimal

    Jul 20, 24 10:38 AM

    Representing decimals on number line shows the intervals between two integers which will help us to increase the basic concept on formation of decimal numbers.

    Read More

  5. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 20, 24 01:11 AM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More