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BINARY TO DECIMAL AND DECIMAL TO BINARY CONVERSION
Kashan Haider Kashan Haider in Programming
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How to Convert Binary to Decimal and Decimal to Binary

Binary System

The binary numbering system is used in computer systems or electronic devices for storage, transfer and manipulation of data, It. is a method of mathematical expression that uses only two symbols: typically “0” and “1”. The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit or binary digit. 

BINARY SYSTEM

Most Significant Bit (MSB) and Least Significant Bit (LSB)

For a binary number, the most significant bit (MSB) is the digit furthermost to the left of the number and the least significant bit (LSB) is the rightmost digit.

MSB AND LSB DEMONSTRATION

Convert from Decimal to Binary

If you do not have any access to a calculator, the residual method can be used to convert a decimal number into binary. This involves iteratively dividing the number by 2 till you get to 0 while taking note of each remainder.

  1. Write down the decimal numbers.
  2. Continually divide decimal numbers by 2 until the final result equals zero.
  3. Keep noting the remainder on the right hand side, this will be  either a “1” or a “0” 
  4. The binary result is achieved by arranging all the remainders in order, with the least significant bit (LSB) at the top and the most significant bit (MSB) at the bottom.

THE FOLLOWING IMAGE IS THE PRACTICAL OF CONVERTING DECIMAL 183 INTO BINARY.

DECIMAL TO BINARY PRACTICAL

IN THE EXAMPLE ABOVE WE LEARNT HOW TO CONVERT DECIMAL 183 INTO BINARY, WE LEARNT THAT DECIMAL 183 = 10110111

Convert Binary to Decimal

Converting from binary to decimal involves multiplying the value of each digit (i.e. 1 or 0) by the value of the placeholder in the number

  1. Write down the number.
  2. Starting with the LSB, multiply the digit by the value of the place holder.
  3. Continue doing this until you reach the MSB.
  4. Add the results together.
BINARY TO DECIMAL PRACTICLE

Some Basic Problems/Questions:

For each question, choose the best answer. The answer key is below.

  1. Convert 128 into binary?
    • 100001000
    • 1000000
    • 010000100
    • 10000000
  2. What is 100101100 in decimal?
    • 255
    • 256
    • 184
    • 300

If you could calculate the correct answer then comment on this post and let others know, You’re a genius.

Answer Key

  1. 10000000
  2. 183

Have a question or confusion related to this article? comment below

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Written By
Kashan Haider
Kashan Haider

I love to learn new technologies and implement my ideas in the real world,
I like teaching too, Sharing my knowledge is one of my hobbies.
Talk to me about programming, coding or hacking and you're my friend!

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