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How to Convert Decimal to Binary and Binary to Decimal

Binary System

The binary numbering system is the basis for storage, transfer and manipulation of data in computer systems and digital electronic devices. This system uses base 2 rather than base 10 which we are familiar with for counting in everyday life.

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

Steps to Convert from Decimal to Binary

If you don’t have a calculator to hand, you can easily convert a decimal number to binary using the remainder method. This involves dividing the number by 2 recursively until you’re left with 0 while taking note of each remainder.

  1. Write down the decimal number.
  2. Divide the number by 2.
  3. Write the result underneath.
  4. Write the remainder on the right-hand side. This will be 0 or 1.
  5. Divide the result of the division by 2 and again write down the remainder.
  6. Continue dividing and writing down remainders until the result of the division is 1 or 0.
  7. The most significant bit (MSB) is at the bottom of the column of remainders and the least significant bit (LSB) is at the top.
  8. Read the series of 1s and 0s on the right from the bottom up. This is the binary equivalent of the decimal number.

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

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

Steps to 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

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