The , also known as the base 10 system, is the most common numerical system used to represent s in everyday life. However, it is not the only numerical system available for use. Another common numerical system is the system. The binary system only uses two numerals, 0 and 1, making it a base 2 system.

Converting a number from decimal to binary can be an essential skill in computer programming, electronics, and computer science. In this article, we will discuss how to a number from the decimal system to the binary system.

To convert a decimal number to binary, we use the following steps:

Step 1: Divide the decimal number by 2

The first step in converting a decimal number to binary is to divide the decimal number by 2. We carry the remainder to the next step in the process. For example, let’s convert the number 12 to binary.

12 ÷ 2 = 6 Remainder: 0

Step 2: Repeat the division, recording remainders

Next, we take the quotient from the previous step, and divide it by two. Like step 1, we record the remainder and carry it over to the next step.

6 ÷ 2 = 3 Remainder: 0

3 ÷ 2 = 1 Remainder: 1

1 ÷ 2 = 0 Remainder: 1

Step 3: Write down the remainders in reverse order

At this point, we have fully divided the decimal number and have a set of remainders. To get the final binary number, we write down the remainders from step 2 in reverse order.

The remainders for number 12 were: 0, 0, 1, and 1.

So, the binary number representation of 12 is 1100.

Let’s look at another example. Suppose we want to convert the decimal number 23 to binary.

Step 1:

23 ÷ 2 = 11 Remainder: 1

Step 2:

11 ÷ 2 = 5 Remainder: 1

5 ÷ 2 = 2 Remainder: 1

2 ÷ 2 = 1 Remainder: 0

1 ÷ 2 = 0 Remainder: 1

Step 3:

The remainders for the number 23 were: 1, 1, 1, 0, and 1.

So, the binary representation of 23 is 10111.

Now, what if the decimal number has a decimal point? The process of converting decimal with a decimal point to binary is slightly different. We follow the same process as above but separately convert the integer part and the fractional part of the decimal number.

Suppose we want to convert the decimal number 10.25 to binary. First, we convert the integer part of the number (10) and then the fractional part (0.25) separately.

Integer part (10):

10 ÷ 2 = 5 Remainder: 0

5 ÷ 2 = 2 Remainder: 1

2 ÷ 2 = 1 Remainder: 0

1 ÷ 2 = 1 Remainder: 1

The binary number of the integer part of 10 is 1010.

Fractional part (0.25):

Multiplying by 2: 0.25 x 2 = 0.50 Integer Part: 0

Multiplying by 2: 0.50 x 2 = 1.00 Integer Part: 1

The binary representation of the fractional part of 0.25 is 01.

So the final binary representation of 10.25 is: 1010.01.

In conclusion, converting a number from decimal to binary requires division and the recording of remainders until all the digits are converted. The conversion process can be done in steps as explained above. By learning how to convert decimal to binary, one can make computations more efficient and understand how computers and electronic devices manipulate data.

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