Or just std::bitset<8> for C++. Bit fields are neat though, it can store weird stuff like a 3 bit integer, packed next to booleans

You beat me to it!

This was gonna be my response to OP so I'll offer an alternative approach instead:

typedef enum flags_e : unsigned char {
  F_1 = (1 << 0),
  F_2 = (1 << 1),
  F_3 = (1 << 2),
  F_4 = (1 << 3),
  F_5 = (1 << 4),
  F_6 = (1 << 5),
  F_7 = (1 << 6),
  F_8 = (1 << 7),
} Flags;

int main(void) {
  Flags f = F_1 | F_3 | F_5;
  if (f & F_1 && f & F_3) {
    // do F_1 and F_3 stuff
  }
}