A binary number is divisible by 2 if its last bit is zero.
Understanding Divisibility by 2 in Binary
Just like in the decimal system, there's a simple trick to determine divisibility by 2 in the binary system (base-2).
The Rule: Check the Last Bit
According to the reference provided:
- How can we say if a given binary number is divisible by 2? Just check if the last bit is zero. (06-Jan-2014)
This means:
- If the rightmost bit (the least significant bit) of a binary number is 0, the number is divisible by 2.
- If the last bit is 1, the number is not divisible by 2.
Why Does This Work?
Binary numbers represent values as powers of 2. From right to left, the place values are 20, 21, 22, 23, and so on. That means:
- The rightmost bit represents 20, which is 1.
- All other bits represent powers of 2 that are greater than or equal to 2.
If the last bit is 0, it means there are zero "ones" in the number. The rest of the number consists of multiples of 2, and therefore the whole number is a multiple of 2.
Examples
Here are a few examples to illustrate the concept:
- 1010: Last bit is 0. This is divisible by 2 (10 in decimal).
- 1100: Last bit is 0. This is divisible by 2 (12 in decimal).
- 1011: Last bit is 1. This is not divisible by 2 (11 in decimal).
- 1111: Last bit is 1. This is not divisible by 2 (15 in decimal).
- 1000: Last bit is 0. This is divisible by 2 (8 in decimal).
Practical Application
This rule is useful in various computing scenarios, such as:
- Bitwise Operations: Determining if a number is even or odd for optimization purposes.
- Data Processing: Filtering data based on divisibility rules.
- Low-Level Programming: Implementing efficient algorithms that rely on the properties of binary numbers.
