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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