Bit Math

What are bits?

Bits are 0s and 1s, the “binary” language you hear about a lot. It’s very similar to our daily usage of digits, it only goes up to 1 instead of 9.

Normal counting, base 10

0, 1, 2, 3, 4, 5,..

Binary counting, base 2

0, 1, 10, 11, 100, 101, 110…

Knowing the exact values of numbers in binary isn’t really relevant to Lua, but it IS important to know for bit mathematics.

Treat binary numbers like they’re normal numbers, just use “2” when you would use “10”. 110 isn’t 10² + 10¹ + 0, for example. It’s 2² + 2¹ + 0, which is 6.

Bit shifting

x << 3 means shifting x three digits to the left, which means adding three 0s to its right. This is the same as multiplying it by 2^3 = 8. Very similar to how we multiply by 1000 to add three 0s in normal mathematics.

1110 (14 = 8 + 4 + 2) becomes 1110000 (112 = 64 + 32 + 16).

x >> 3 means shifting x three digits to the right, which means removing the last three digits, regardless of their value. This is the same as dividing it by 2³ = 8. Yes, this means we can lose accuracy in our number, that’s the truth of math without going into floating point representations.

1010 (10) becomes 1 (1). Divided by 8, the result is 1, and the remainder (2) is lost forever.

Upper / Lower Bits

When a SOC Action makes mention of Upper / Lower 16 bits, it’s referring to values over and under 65536, respectively. 65536 = 2¹⁶, which is where the 16 comes from.

If you enter a value of “2048”, that’s the lower 16 bits. 2048 is 2^11, so in binary, we can represent it with a 1 followed by eleven zeroes. Sort of like how we represent

0000 0000 0000 0000 0000 1000 0000 0000

If you enter a value of “2048 << 16”, you shift it 16 digits to the left, which is the same as multiplying it by 2¹⁶, which is 65536. At this point:

0000 1000 0000 0000 0000 0000 0000 0000

2048 has become your UPPER value. If you want an upper value of 1, and a lower value of 2048, for example, you would write:

2048 + 1 << 16

Alternatives: The constant FRACBITS seems to be designed for this purpose. The expressions 3 << 16 and 3 << FRACBITS are exactly the same thing. The constant FRACUNIT is 65536, which equals 1 << 16. The expressions 3 << 16 and 3 * FRACUNIT are also exactly the same thing.