How to Convert Decimal to Binary

How to Convert Decimal to Binary and vise versa is crucial to master, such skills will give you the confidence when you deal with Network and Storage devices. Mastering Network topics such IP Addressing Subnetting, Speed measurements Megabits (Mb) and Gigabits (Gb), or even Storage measurements such MegaByte (MB), GigaByte (GB), and TeraByte (TB), requires you understand and master how to convert back and fourth between the 3 base numbers: 10, 2, and 16.

Converting Decimal to Binary

At first, it might look tricky to plug all pieces together, but once you practice few times, it will be so easy to understand the process and come up with the answer right away. I have listed few examples for you to go through, however, and after you are done, pick your own few numbers and convert them to binary.

E.g. Convert 212 decimal to binary

Step 1: Write down the Binary chart on a piece of paper. Start from 1 up to 128. If the decimal number bigger than 256, write 256 after 128, if it’s bigger than 512, write 512 after 256, and so on.

128  64  32  16  8  4  2  1

Step 2: subtraction operation. Starting from the left side, subtract the place value from the given decimal number. If you were able to subtract the place value from the given decimal number, write 1 under this value. If you were not able to subtract the place value from the given decimal number, write 0 under that place value. Follow the detailed subtraction steps below. 

Remember: We are subtracting the Binary Place Values from the given Decimal number which in our case 212, till this decimal number Zeros Out and no more subtraction can be done.

Detailed Subtraction Steps

a. Ask yourself, would 128 place value goes into decimal number 212? Yes! write 1 under 128, therefore, 212 – 128 = 84 as remainder, take it and move on to the next Binary place Value.

b. Would 64 place goes into 84? Yes! write 1 under 64 and subtract 84 – 64 = 20 again as remainder.

c. 32 won’t go into 20, write 0 under 32 and move on with the remainder 20 to the next place.

d. 16 goes into 20, write 1 under 16 and subtract 20 – 16 = 4

e. 8 won’t go into 4, write 0 under and 8 and move on with the remainder 4 to the next place.

f. 4 goes into 4, write 1 under 4 and subtract 4 – 4 = 0 >> Bingo! 212 Decimal Number Zeroed Out.

g. Remember: If the decimal number zeros out on the middle of the chart, write zeros under the rest of the places.

128  64  32  16  8  4  2  1
  1   1   0   1  0  1  0  0

Step 3: Verify – Add only the ON places: 128 + 64 + 16 + 4 = 212

Therefore, 212 decimal equal to 11010100.

Note: I am going to minimize the steps at the next examples to expedite the process.

Convert 83 Decimal to Binary

Step 1: write down the binary chart on a piece of paper.

Step 2: subtract the binary places from the decimal number one by one. If positive write 1, and if negative write 0. After you done, you should have similar to the following chart.

128  64  32  16  8  4  2  1
  0   1   0   1  0  0  1  1 

Step 3: add only the ON places: 64 + 16 + 2 + 1 = 83

Always drop the leading Zeros from the left side.

Therefore, 83 decimal equal to 1010011.

Convert 199 Decimal to Binary

Step 1: write down the binary chart on a piece of paper.

Step 2: subtract the binary places from the decimal number. After you done, you should have similar to the following chart:

128  64  32  16  8  4  2  1
  1   1   0   0  0  1  1  1 

Step 3: add only the ON places: 128 + 64 + 4 + 2 + 1 = 199

Therefore, 199 decimal equal to 11000111.

Convert 603 Decimal to Binary

Step 1: write down the binary chart on a piece of paper:

Step 2: subtract the binary places from the decimal number. 

1024  512  128  64  32  16  8  4  2  1
   0    1    0   1   0   1  1  0  1  1 

Step 3: add only the ON places: 512 + 64 + 16 + 8 + 2 + 1 = 603

Therefore, 603 decimal equal to 1001011011.

Convert 186 Decimal to Binary

Step 1: write the down the binary chart on a piece of paper.

Step 2: subtract the binary places from the decimal number.

128  64  32  16  8  4  2  1
  1   0   1   1  1  0  1  0 

Step 3: add only the ON places: 128 + 32 + 16 + 8 + 2 = 186

Therefore, 186 decimal equal to 10111010.

Decimal to Binary Chart

After this practice, you should be able to know by heart all decimal value in Binary from 0 (0000) up to 15 (1111).

• 0 = 0000
• 1 = 0001
• 2 = 0010
• 3 = 0011
• 4 = 0100
• 5 = 0101
• 6 = 0110
• 7 = 0111
• 8 = 1000
• 9 = 1001
• 10 = 1010
• 11 = 1011
• 12 = 1100
• 13 = 1101
• 14 = 1110
• 15 = 1111

Subject Related

By Wikipedia Decimal | Math is Fun | Numbers Better Explained | Free Online Calculator | How to Master CCNA | R&S ICND1 and ICND2 | Network Warrior | CCNA R&S Study Guide | R&S 200-120 Official Guide | Routing and Switching Guide