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Lesson 4 Convert Decimal to Binary
Objective Convert numbers between decimal and binary

Converting Decimal to Binary

Converting a decimal number to its binary equivalent is a little more challenging. Here's one approach.
  1. Find the highest power of 2 less than or equal to the decimal number. In your binary number, place a 1 in the position corresponding to this power of 2.
  2. Subtract the power of 2 found in step 1 from the decimal number to obtain a new decimal number. If the new decimal number is 0, then you are done; otherwise, return to step 1 with the new decimal number.

Click through the following SlideShow to convert the decimal number 204 to binary.


  1. The largest power of 2 less than or equal to 204 is 2 raised to the 7th = 128.
  2. Subtracting 128 from 204 gives 76. The largest power of 2 less than or equal to 76 is 2 raised to the 6th = 64.
  3. Subtracting 64 from 76 gives 12. The largest power of 2 less than or equal to 12 is 2 raised to the 3 = 8.
  4. Subtracting 8 from 12 gives 4. The largest power of 2 less than or equal to 4 is 2^2 =4.
  5. Subtracting 4 from 4 givess 0. We are completed.
  6. From our work we see that the binary equivalent of 204 should have 1s in the corresponding to 2^7, 2^6, 2^3 and 2^2.

Converting From Decimal to Binary
Binary numbers can require many digits. In the next lesson, you will look at how binary numbers can be expressed more compactly using hexadecimal form.

Converting Binary Numbers - Quiz

Click the Quiz link below to see how well you understand binary numbers.
Converting Binary Numbers - Quiz