Decimal to Binary Conversion

Before I take you through the rules, on how to convert decimal to binary, I will brief you on these two types of number systems; binary and decimal. 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 is a binary number 1010, which can be written as 1010₂. 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 10₁₀ and read as 'ten, base ten'.

Rules on How To Convert Decimal To Binary

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.

Convert the Following Decimals Numbers To their Binary Forms

10

10 ÷ 2 = 5, remainder is 0
5 ÷ 2 = 2, remainder is 1
2 ÷ 2 = 1, remainder is 0
1 ÷ 2 = 0, remainder is 1

Now the division stops here, as there is nothing to divide further by 2. So, as I said, 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, 10₁₀ = 1010₂.

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

100

100 ÷ 2 = 50, remainder is 0
50 ÷ 2 = 25, remainder is 0
25 ÷ 2 = 12, remainder is 1
12 ÷ 2 = 6, remainder is 0
6 ÷ 2 = 3, remainder is 0
3 ÷ 2 = 1, remainder is 1
1 ÷ 2 = 0, remainder is 1

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

Thus, 100₁₀ = 1100100₂.

190

190 ÷ 2 = 95, remainder is 0
95 ÷ 2 = 47, remainder is 1
47 ÷ 2 = 23, remainder is 1
23 ÷ 2 = 11, remainder is 1
11 ÷ 2 = 5, remainder is 1
5 ÷ 2 = 2, remainder is 1
2 ÷ 2 = 1, remainder is 0
1 ÷ 2 = 0, remainder is 1

So, 190₁₀ = 10111110₂.

356

356 ÷ 2 = 178, remainder is 0
178 ÷ 2 = 89, remainder is 0
89 ÷ 2 = 44, remainder is 1
44 ÷ 2 = 22, remainder is 0
22 ÷ 2 = 11, remainder is 0
11 ÷ 2 = 5, remainder is 1
5 ÷ 2 = 2, remainder is 1
2 ÷ 2 = 1, remainder is 0
1 ÷ 2 = 0, remainder is 1

So, 356₁₀ = 101100100₂.

499

499 ÷ 2 = 249, remainder is 1
249 ÷ 2 = 124, remainder is 1
124 ÷ 2 = 62, remainder is 0
62 ÷ 2 = 31, remainder is 0
31 ÷ 2 = 15, remainder is 1
15 ÷ 2 = 7, remainder is 1
7 ÷ 2 = 3, remainder is 1
3 ÷ 2 = 1, remainder is 1
1 ÷ 2 = 0, remainder is 1

Therefore, 499₁₀ = 111110011₂.

550

550 ÷ 2 = 275, remainder is 0
275 ÷ 2 = 137, remainder is 1
137 ÷ 2 = 68, remainder is 1
68 ÷ 2 = 34, remainder is 0
34 ÷ 2 = 17, remainder is 0
17 ÷ 2 = 8, remainder is 1
8 ÷ 2 = 4, remainder is 0
4 ÷ 2 = 2, remainder is 0
2 ÷ 2 = 1, remainder is 0
1 ÷ 2 = 0, remainder is 1

Hence, 550₁₀ = 1000100110₂.

1256

1256 ÷ 2 = 628, remainder is 0
628 ÷ 2 = 314, remainder is 0
314 ÷ 2 = 157, remainder is 0
157 ÷ 2 = 78, remainder is 1
78 ÷ 2 = 39, remainder is 0
39 ÷ 2 = 19, remainder is 1
19 ÷ 2 = 9, remainder is 1
9 ÷ 2 = 4, remainder is 1
4 ÷ 2 = 2, remainder is 0
2 ÷ 2 = 1, remainder is 0
1 ÷ 2 = 0, remainder is 1

So, 1256₁₀ = 10011101000₂.

1789

1789 ÷ 2 = 894, remainder is 1
894 ÷ 2 = 447, remainder is 0
447 ÷ 2 = 223, remainder is 1
223 ÷ 2 = 111, remainder is 1
111 ÷ 2 = 55, remainder is 1
55 ÷ 2 = 27, remainder is 1
27 ÷ 2 = 13, remainder is 1
13 ÷ 2 = 6, remainder is 1
6 ÷ 2 = 3, remainder is 0
3 ÷ 2 = 1, remainder is 1
1 ÷ 2 = 1, remainder is 1

So, 1789₁₀ = 11011111101₂.

1599

1599 ÷ 2 = 799, remainder is 1
799 ÷ 2 = 339, remainder is 1
399 ÷ 2 = 199, remainder is 1
199 ÷ 2 = 99, remainder is 1
99 ÷ 2 = 49, remainder is 1
49 ÷ 2 = 24, remainder is 1
24 ÷ 2 = 12, remainder is 0
12 ÷ 2 = 6, remainder is 0
6 ÷ 2 = 3, remainder is 0
3 ÷ 2 = 1, remainder is 1
1 ÷ 2 = 1, remainder is 1

Hence, 1599₁₀ = 11000111111₂.

1999

1999 ÷ 2 = 999, remainder is 1
999 ÷ 2 = 499, remainder is 1
499 ÷ 2 = 249, remainder is 1
249 ÷ 2 = 124, remainder is 1
124 ÷ 2 = 62, remainder is 0
62 ÷ 2 = 31, remainder is 0
31 ÷ 2 = 15, remainder is 1
15 ÷ 2 = 7, remainder is 1
7 ÷ 2 = 3, remainder is 1
3 ÷ 2 = 1, remainder is 1
1 ÷ 2 = 0, remainder is 1

Thus, 1999₁₀ = 11111001111₂.

After reading the above examples, I am 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!