The most fundamental way to check even/odd

july 2026

What could be the most fundamental way to determine whether a number is even or odd without using the modulo (%) operator? Bits (0/1) the "language of computers," and the only thing a computer TRULY understands.

But how!! how can we determine whether the number is odd or even using just those two digits or some combination of them ?? We will see it gradually...

Definition of odd and even :

Back in the school/college days we were taught that just like decimal number we can perform arithmetic operations on binary numbers as well: we can do addition, subtraction, division, multiplication and so on... Later, in programming, we also learned that binary numbers can be manipulated using bitwise operators,which work on each 0 and 1 separately i.e they operate on thier individual bits. learn more

The table below demonstrates the AND, OR, and XOR bitwise operations.

Now that we have covered the basic concepts, let's see the implementation.

1] The Decimal/Common Approach:

Steps :

1. take input from user .
2. divide it by 2
3. if its completely divisible by 2 (as said earlier) we return "Even" if its not we return "Odd", as simple as that .

Here is the python program :

what we used here :

1. A decimal number (n)
2. Modulo Operator (%)
3. Divsior (2)
4. Comparison Operator (==).

2.1] Binary/fundamental Approach:

Before talking about logic itself , lets understand how it works:
Its all about Observation. look at the image below did you notice something? Every EVEN number has 0 in the 2⁰ position and for ODD its 1.

so let's try to program it!!

Steps:

1. take a number as input from user .
2. convert that number into binary using 'bin()' function in python and store it in variable or don't . it will return string for e.g : 4 will be equals "100"
3. compare the last string character with "0"
4. if the last character is "0" , function will return "Even" otherwise "Odd".

Here is the program:

what we used here :

1. A decimal number (n)
2. python's inbuilt function - bin()
3. Negative Indexing [-1]
4. Comparison Operator (==).

2.2] Bitwise AND (&) Approach :

Earlier, we talked about bitwise operators, but Program 2.1 didn't use any of them.Well, That was just one approach. Now let's do it using bitwise AND (&).

Steps:

1. First, take a number as input from the user.
2. perform a bitwise AND operation between the number and 1 (i.e n & 1).
3. If the result is 0, the last bit is 0, which means the number is Even.
4. Otherwise, number is Odd asss simple as that.

Here is the program:

Things to notice here :

• We didn't convert the input to binary this time. Why? Because if we did convert it explicitly using the bin() function, it would return something like "0b10101...". If we then tried to convert it into an integer directly, the program will throw an error because the string contains "0b" (It simply indicates that the number is in binary form).
• Someone: "What if we perform a bitwise operation on a string, for e.g, "0b0101" & "0001" ?"
  We can't, because, as the name suggests, it's a bitwise operator, and it does not work on strings directly. But if you know how to strip a string so that the left part ("0b") and the right part ("0101") get separated, then you can go that way as well by converting "0101" back into an integer .

What we used here :

1. A decimal number (n)
2. Bitwise AND operator (&)
3. Our main character/number (1)
4. Comparison operator (==)

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