[Squaring, Cubing & Powers] 2^24 Challenge

Shifting a number by 1 to the left is equal to a multiplication by the base you’re working with (multiplication by 10 in base 10, multiplication by 2 in binary, multiplication by 16 in hexadecimal, and so on).
Starting with a value of 1, the number of times you shift to the left is the same as an exponent of your base (ex: 1 << 1 == 10, whether in binary or in base 10).
Since we’re multiplying twos, binary operations would be ideal.

So we simply take 1 and binary-shift it to the left 24 times, making it the same as 2^24.
Assuming we’re coding in C# and using an int (32bits should be quite enough to avoid overflowing in this case):
var result = 1 << 24;
That way, instead of making 23 multiplications by calculating an exponent, we simply look at the binary expression of 1 followed by 24 zeroes (1 0000 0000 0000 0000 0000 0000), which is how the int is stored as anyway.

When converted back to base 10, we get the answer 16 777 216 (which some will recognize as just 1 more than the largest unsigned integer that can be represented with 24 bits).

Thank you for this explanation!