Binary Number System

Here we will discuss about the binary number system we already know binary numbers play a vital role in the design of digital computers.

Hence a detailed discussion of binary number system is given in this section. Binary number system uses two symbols 0 and 1 and its radix is 2. The symbols 0 and 1 are generally called BITS which is a contraction of the two words Binary digits.

An n-bit binary number of the form an-1 an-2 ….. a1 a0 where each ai (i = 0, 1, …. n - 1) is either 0 or 1 has the magnitude.

an-1 2n-1 + an-2 2n-2 + …….+ a1 21 + a020.

For fractional binary numbers, the base has negative integral powers starting with -1 for the bit position just after the binary point.

The bit at the extreme left of a binary number has the highest positional value and is usually called the Most Significant Bit or MSB. Similarly, the bit occupying the extreme right position of a given binary number has the least positional value and is referred to as the Least Significant Bit or LSB.

To facilitate the distinction between different number systems, we generally use the respective radix as a subscript of the number. However the subscript will not be used when there is no scope of confusion.


In binary number system a few examples on binary numbers and their decimal equivalents are given below:

1011012 = 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20

= 32 + 0 + 8 + 4 + 0 + 1

= 4510

The above results can be more clearly expressed in the following manner:
examples on binary numbers

Binary point

111.10112

= 1 × 22 + 1 × 21 + 1 × 20 + 1 × 2-1 + 0 × 2-2 + 1 × 2-3 + 1 × 2-4

= 4 + 2 + 1 + .5 + 0 + .125 + .0625

= 7.687510

The above results can be more clearly expressed in the following manner:

These are the basic examples shown above.

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 Number System 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