Rajib Singha
May 6, 2019

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Decimal to binary conversion is about division, subtraction, and moving upward. Confused? Get started with this by practicing some easy problems and understand this concept in a few simple steps.

Before understanding decimal to binary conversion, you need to understand these two types of number systems. The binary number system is also known as the base-2 number system, as it represents numeric values using only two symbols; **1** and **0**. Example, the number 1010, which can be written as 1010_{2}.

The decimal number system, or base-10 number system, as it is known, is the most commonly-used number system. It has ten possible values starting from **0 - 9**, for each place value. For example, the number 10 can be written as 10_{10} and read as 'ten, base ten'.

The rule is to divide a given decimal number by 2 and make a note of the remainder. Continue dividing, until you cannot divide by 2 anymore. When you note down the remainders starting from the bottom, you get the binary number. The rule is simple and you will get a hold of it by the help of the following examples.

10 ÷ 2 = 5, remainder is

5 ÷ 2 = 2, remainder is

2 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

Now the division stops here, as there is nothing to divide further by 2. So, starting from the bottom, write down the remainders and work your way up the list. In this case, it will be 1010 (starting from the bottom remainder). Thus, 10

This example must have helped you to grasp the idea. The following examples include some miscellaneous numbers with greater values, to help you understand the concept better.

100 ÷ 2 = 50, remainder is

50 ÷ 2 = 25, remainder is

25 ÷ 2 = 12, remainder is

12 ÷ 2 = 6, remainder is

6 ÷ 2 = 3, remainder is

3 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

So, you have the answer as 1100100 (starting from the bottom).

Thus, 100

190 ÷ 2 = 95, remainder is

95 ÷ 2 = 47, remainder is

47 ÷ 2 = 23, remainder is

23 ÷ 2 = 11, remainder is

11 ÷ 2 = 5, remainder is

5 ÷ 2 = 2, remainder is

2 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

So, 190

178 ÷ 2 = 89, remainder is

89 ÷ 2 = 44, remainder is

44 ÷ 2 = 22, remainder is

22 ÷ 2 = 11, remainder is

11 ÷ 2 = 5, remainder is

5 ÷ 2 = 2, remainder is

2 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

So, 356

249 ÷ 2 = 124, remainder is

124 ÷ 2 = 62, remainder is

62 ÷ 2 = 31, remainder is

31 ÷ 2 = 15, remainder is

15 ÷ 2 = 7, remainder is

7 ÷ 2 = 3, remainder is

3 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

Therefore, 499

550 ÷ 2 = 275, remainder is

275 ÷ 2 = 137, remainder is

137 ÷ 2 = 68, remainder is

68 ÷ 2 = 34, remainder is

34 ÷ 2 = 17, remainder is

17 ÷ 2 = 8, remainder is

8 ÷ 2 = 4, remainder is

4 ÷ 2 = 2, remainder is

2 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

Hence, 550

1256 ÷ 2 = 628, remainder is

628 ÷ 2 = 314, remainder is

314 ÷ 2 = 157, remainder is

157 ÷ 2 = 78, remainder is

78 ÷ 2 = 39, remainder is

39 ÷ 2 = 19, remainder is

19 ÷ 2 = 9, remainder is

9 ÷ 2 = 4, remainder is

4 ÷ 2 = 2, remainder is

2 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

So, 1256

1789 ÷ 2 = 894, remainder is

894 ÷ 2 = 447, remainder is

447 ÷ 2 = 223, remainder is

223 ÷ 2 = 111, remainder is

111 ÷ 2 = 55, remainder is

55 ÷ 2 = 27, remainder is

27 ÷ 2 = 13, remainder is

13 ÷ 2 = 6, remainder is

6 ÷ 2 = 3, remainder is

3 ÷ 2 = 1, remainder is

1 ÷ 2 = 1, remainder is

So, 1789

1599 ÷ 2 = 799, remainder is

799 ÷ 2 = 339, remainder is

399 ÷ 2 = 199, remainder is

199 ÷ 2 = 99, remainder is

99 ÷ 2 = 49, remainder is

49 ÷ 2 = 24, remainder is

24 ÷ 2 = 12, remainder is

12 ÷ 2 = 6, remainder is

6 ÷ 2 = 3, remainder is

3 ÷ 2 = 1, remainder is

1 ÷ 2 = 1, remainder is

Hence, 1599

1999 ÷ 2 = 999, remainder is

999 ÷ 2 = 499, remainder is

499 ÷ 2 = 249, remainder is

249 ÷ 2 = 124, remainder is

124 ÷ 2 = 62, remainder is

62 ÷ 2 = 31, remainder is

31 ÷ 2 = 15, remainder is

15 ÷ 2 = 7, remainder is

7 ÷ 2 = 3, remainder is

3 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

Thus, 1999

These numbers were all whole numbers. If you encounter a fraction, you need to know how to convert it to the resultant form. The process is very simple, you need not panic. If you come across a number, like, say, 14.625, all you have to do is consider the part after and before the decimal point as two separate entities.

This means, that you must convert 14 and 0.625 in a different manner. So, first, convert 14 in the same manner as described earlier.

14 ÷ 2 = 7, remainder is**0**

7 ÷ 2 = 3, remainder is**1**

3 ÷ 2 = 1, remainder is**1**

1 ÷ 2 = 0, remainder is**1**

Thus, 14_{10} = 1110_{2}.

14 ÷ 2 = 7, remainder is

7 ÷ 2 = 3, remainder is

3 ÷ 2 = 1, remainder is

1 ÷ 2 = 0, remainder is

Thus, 14

Now, we have to get the binary equivalent of 0.625. For this, what you need to do is multiply it by 2. If the resultant answer has **1** before the point, note down 1. Or else note down 0. And form the number in this manner. Continue until the part after the point is 0.

Remember, while multiplying the answers with 2 again, you do not have consider the part before the point, only the part after the point will be considered.

0.625 * 2 = 1.25, note down**1**

0.25 * 2 = 0.5, note down**0**

0.5 * 2 = 1.0, note down**1**

Now that the part after the point is zero, you need to stop here.

Thus, 0.625_{10} = 0.101_{2}.

Therefore, 14.625_{10} = 1110.101_{2}.

0.625 * 2 = 1.25, note down

0.25 * 2 = 0.5, note down

0.5 * 2 = 1.0, note down

Now that the part after the point is zero, you need to stop here.

Thus, 0.625

Therefore, 14.625

After reading these examples, we are certain that you will be able to get yourself acquainted with the method of converting decimal to binary. And, once you are good with the technique, you will be able to work with any given numbers. Cheers!