Why we divide decimal by 2 to get binary? What does division by two represent when dealing with binary?

When we convert a decimal number to binary by dividing by 2, the process fundamentally reflects how the binary number system works. Each time we divide by two, we take away the last digit, and the rest becomes the new number. Dividing a binary number by two is like moving the digits to the right.

For example, if we shift 1001 to the right, it becomes 100, and the 1 at the end is removed.

Here’s an example using the number 23 to explain the conversion from decimal to binary:

23 ÷ 2 = 11, remainder 1
11 ÷ 2 = 5, remainder 1
5 ÷ 2 = 2, remainder 1
2 ÷ 2 = 1, remainder 0
1 ÷ 2 = 0, remainder 1
When the number reaches zero, you read the remainders from bottom to top, giving the binary number: 10111.

Now, let’s see the same thing directly with binary:
10111 ÷ 2 = 1011, remainder 1
1011 ÷ 2 = 101, remainder 1
101 ÷ 2 = 10, remainder 1
10 ÷ 2 = 1, remainder 0
1 ÷ 2 = 0, remainder 1

Let’s see it with another lens, 👁️

The concept with shifting binary numbers to the right:
10111 shifted right = 1011, with 1 falling off
1011 shifted right = 101, with 1 falling off
101 shifted right = 10, with 0 falling off
10 shifted right = 1, with 0 falling off
1 shifted right = 0, with 1 falling off
This shows how dividing by 2 removes the last binary digit each time, with the remainder giving the dropped digit.

We rearrange the remainders from bottom to top in the binary conversion process because each remainder (falling off number) represents the least significant bits first.

Here’s why:
🔹 The first remainder (falling off number) we get from dividing by 2 the first time represents the smallest binary place value, which is the rightmost bit (also called the least significant bit or LSB).
🔹 The next remainder (falling off number) comes from the next division, and it represents the next place value in the binary number.
🔹 As you keep dividing, each new remainder represents a higher place value, so the last remainder (falling off number) you get corresponds to the leftmost bit (the most significant bit or MSB).

By reading the remainders in reverse (bottom to top), we build the binary number correctly from the least significant to the most significant bit.