Convert a non-negative integer to its binary string representation without using built-in conversion methods. Binary representation uses only 0s and 1s, where each position represents a power of 2.

In Salesforce development, understanding binary operations is useful for permission sets, bitmasking operations, or custom encoding scenarios in integrations.

Examples:

Input: num = 0 Output: "0" Explanation: Zero in binary is represented as "0" Input: num = 5 Output: "101" Explanation: 5 in decimal is 101 in binary (4 + 0 + 1 = 5) Input: num = 255 Output: "11111111" Explanation: 255 in decimal is 11111111 in binary (128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255)
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