216 in Binary
2026-02-28 17:34 Diff
https://brightchamps.com/en-us/math/numbers/216-in-binary

There are certain rules to follow when converting any number to binary. Some of them are mentioned below:

Rule 1: Place Value Method

This is one of the most commonly used rules to convert any number to binary. The place value method is the same as the expansion method, where we need to find the largest power of 2. Let’s see a brief step-by-step explanation to understand the first rule.

Find the largest power of 2 less than or equal to 216.

Since the answer is 27, write 1 next to this power of 2.

Subtract the value (128) from 216. So, 216 - 128 = 88.

Find the largest power of 2 less than or equal to 88.

The answer is 26. So, write 1 next to this power. 88 - 64 = 24.

Find the largest power of 2 less than or equal to 24.

The answer is 24. So, write 1 next to this power. 24 - 16 = 8.

Find the largest power of 2 less than or equal to 8.

The answer is 23. So, write 1 next to this power. 8 - 8 = 0.

Since there is no remainder, we can write 0 next to the remaining powers (25, 22, 21, and 20).

Final conversion will be 11011000.

Rule 2: Division by 2 Method

The division by 2 method is the same as the grouping method. A brief step-by-step explanation is given below for better understanding.

First, 216 is divided by 2 to get 108 as the quotient and 0 as the remainder.

Now, 108 is divided by 2. Here, we will get 54 as the quotient and 0 as the remainder.

Dividing 54 by 2, we get 0 as the remainder and 27 as the quotient.

Divide 27 by 2 to get 1 as the remainder and 13 as the quotient.

Dividing 13 by 2, we get 1 as the remainder and 6 as the quotient.

Dividing 6 by 2, we get 0 as the remainder and 3 as the quotient.

Dividing 3 by 2, we get 1 as the remainder and 1 as the quotient.

Dividing 1 by 2, we get 1 as the remainder and 0 as the quotient.

We stop the division once the quotient becomes 0.

Now, we write the remainders upside down to get the binary equivalent of 216, 11011000.

Rule 3: Representation Method

This rule also involves breaking the number into powers of 2.

Identify the powers of 2 and write them down in decreasing order i.e., 27, 26, 25, 24, 23, 22, 21, and 20.

Find the largest power that fits into 216. Repeat the process and allocate 1s and 0s to the suitable powers of 2.

Combine the digits (0 and 1) to get the binary result.

Rule 4: Limitation Rule

The limitation of the binary system is that only 0s and 1s can be used to represent numbers.

The system doesn’t use any other digits other than 0 and 1.

This is a base 2 number system, where the binary places represent powers of 2.

So, every digit is either a 0 or a 1.

To convert 216, we use 0s for 25, 22, 21, and 20, and 1s for 27, 26, 24, and 23.