Introduction: How to Convert From Decimal to Binary

Picture of How to Convert From Decimal to Binary

In this Instructable, you will learn how to convert numbers from decimal to binary. Decimal numbers can have the values 0-9 for each place-value. Binary numbers are only made up of the values 0 and 1.

While decimal numbers are used often in everyday life, binary is mostly limited to computer science and engineering.

This Instructable should take you about 10 minutes to read and understand if you are a beginner in the subject.

Materials Needed:

  • Calculator
  • Pen
  • Paper

Step 1: Draw Your Table

Picture of Draw Your Table

First, you draw a t-shaped table like the one shown in Figure 1.

Step 2: Pick a Decimal Number to Convert to Binary

Picture of Pick a Decimal Number to Convert to Binary

1. Choose a decimal number you want to convert to binary and write it in the top-left of the table header.

  • For this Instructable, the number 139 is chosen as an example, as shown in Figure 2.

2. Write "/2" in the top-right of the table header.

Step 3: Fill in the First Row

Picture of Fill in the First Row

1. Divide your decimal number by 2 and place the result in the left column. If the result has a remainder, don't include it in the left column.

  • For the example, the operation 139/2 results in a value of 69.5, as shown in Figure 3.

2. Place the remainder (0 or 1) of your result in the right column. Values that end in ".5" have a remainder of 1 and those that end in ".0" have a remainder of 0.

  • For the example, 69.5 has a remainder of 1, as shown in Figure 3.

Step 4: Fill in the Next Row

Picture of Fill in the Next Row

1. Divide your result from the previous row by 2 to get your new result. Again, don't include the remainder in the left column.

2. Place the remainder of your new result in the right column.

Step 5: Repeat Step 4

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Repeat Step 4 until you get a result of 0 in the left column, as shown in Figure 5.

Step 6: Get Your Result

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1. The original decimal number you chose is now a binary number in the right column, as shown in Figure 6.

2. Write the binary number from bottom to top, as shown by the red arrow in Figure 6.

  • For the example, the decimal number 139 is equal to the binary number 10001011.

Step 7: Summary

To recap, getting a binary number from a decimal number is just a process of successive division by 2. You get the binary number from the remainder of the divisions.

The reason you divide by 2 is because binary is base 2. If you wanted an answer in a different base, such as base 16, you would divide by 16 instead of 2.

Step 8: Other Resources

The links below will take you to different sites where you can learn more about binary and other numeral systems.

  • This link will take you to the Wolfram MathWorld to learn more about binary.
  • This link will take you to Wikipedia to learn how to count in binary
  • This link will take you to Khan Academy, which has videos showing you how to add and multiply in binary.

Comments

LittleFishbo (author)2016-10-20

im just learning binary now, and i am trying to build my own computer (trying),so this REALLY helped me

gm280 (author)2016-04-17

Interesting, but I my add, regardless what your initial decimal number is, a 1 goes into the right hand column for the first division...always. Otherwise the binary equivalent will never match the decimal number. Example, the decimal number eight (8) divided by 2 has no remainder but a 1 goes in the right hand column even those there is no remainder. And it would look like this: 1000 after all the divisions are completed.

Sinther (author)gm2802016-08-01

You forgot that in the end the binary number is read in reverse (bottom to top) so for your example the results in "/2" column will be 0,0,0,1 and the binary 8 will be 1000

norwichnick (author)gm2802016-04-19

Hi gm280. I'm not entirely sure saying that a 1 goes into the right column "always" is the easiest explanation. With the right-most column representing decimal 1, it may be easier for someone to understand this as being set for odd values, whereas even integers would end with a 0. Your values are certainly correct, however.

Mex5150 (author)2016-04-16

Blown away by this, I've been converting to and from binary for years (well, decades really), never seen this method before. I can just do it in my head now, but this is very cool, and I will use it to teach people how to convert ;^>

MissionC8 (author)2016-04-15

Nicely written! I understood every word and had no knowledge of binary till now. Looking at the links currently. Thanks!

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