Convert a Number to Hexadecimal

Bit Manipulation

15 min

Problem Statement

Given an integer num, write an algorithm to convert it to hexadecimal. For negative integers, two’s complement method is used.

Examples

Example 1:

Input: num = 26

Output: "1a"

Example 2:

Input: num = -1

Output: "ffffffff"

Solution (Bitwise Grouping)

We can convert the number by processing its bits in groups of 4, as each hexadecimal digit corresponds to exactly 4 bits (a nibble).

Algorithm Steps

Handle the edge case: if the input is 0, return "0".
Create a mapping from numbers 0-15 to their hex characters ('0'-'9', 'a'-'f').
Initialize an empty result string.
Iterate as long as the number is not zero and we haven't processed all 8 nibbles (for a 32-bit integer).
Get the last 4 bits using a bitwise AND with 15 (which is 1111 in binary): num & 15.
Map this value to its hex character and prepend it to the result string.
Right-shift the number by 4 bits to process the next nibble: num >>= 4.
Return the result string.

Number:

Current Number (Binary)

00000000000000000000000000011010

Current Hex Result

Initial number: 26

Convert to Hex Solution


class Solution:
    def toHex(self, num: int) -> str:
        if num == 0:
            return "0"
        
        hex_map = "0123456789abcdef"
        result = ""
        
        # For negative numbers, we work with the 32-bit two's complement representation
        if num < 0:
            num += 2**32

        while num > 0:
            remainder = num % 16
            result = hex_map[remainder] + result
            num //= 16
            
        return result