Adding two numbers in JavaScript without using the `+` or `-` operators can seem challenging at first glance. However, JavaScript provides various methodologies and bit manipulation techniques that allow us to execute this task. In this article, we delve into bitwise operations, which are low-level operations directly supported by the hardware. Bitwise operations offer a powerful alternative to traditional arithmetic operations.

Utilizing Bitwise Operations

Bitwise AND (`&`), XOR (`^`), and Shift Operators

One approach to adding two numbers without the direct use of `+` or `-` is by employing bitwise operations. The key operators used here are:

• Bitwise AND (`&`): This operator is useful for determining which bits are set in both operands.
• Bitwise XOR (`^`): This acts like addition without carrying. It sets each bit to 1 if only one of the two operands has a 1 in the same position.
• Bitwise Shift (`<<`): This shifts bits to the left, effectively multiplying by two. Useful in carrying operations.

Algorithm

The algorithm to add two numbers using bitwise operators involves:

1. XOR the two numbers. This step simulates addition without carrying.
2. Use the AND operator followed by a left shift to find the carry.
3. Repeat the process with the new values until the carry is zero.

Here's how you can implement it in JavaScript:

• XOR (`a ^ b`): Computes sum without carry. Each bit in the result is 1 if the corresponding bits of `a` and `b` differ, otherwise, it is 0.
• AND followed by Shift (`carry = a & b << 1`): Computes the carry bits. The AND operator identifies which positions carry a bit after addition, and the left shift moves carry 1 position to the left.
• Loop until carry is zero: Continues simulating each carry and adding them back to the sum until no carry remains, showing the operation is complete.