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How can I remove a flag in C?

Short Answer

You want to do an Bitwise AND operation on the current value with a Bitwise NOT operation of the flag you want to unset. A Bitwise NOT inverts every bit (i.e. 0 => 1, 1 => 0).

flags = flags & ~MASK; or flags &= ~MASK;.

Long Answer

ENABLE_WALK  = 0    // 00000000
ENABLE_RUN   = 1    // 00000001
ENABLE_SHOOT = 2    // 00000010
ENABLE_SHOOTRUN = 3 // 00000011

value  = ENABLE_RUN     // 00000001
value |= ENABLE_SHOOT   // 00000011 or same as ENABLE_SHOOTRUN

When you perform a Bitwise AND with Bitwise NOT of the value you want unset.

value = value & ~ENABLE_SHOOT // 00000001

you are actually doing:

      0 0 0 0 0 0 1 1     (current value)
   &  1 1 1 1 1 1 0 1     (~ENABLE_SHOOT)
      ---------------
      0 0 0 0 0 0 0 1     (result)

my.emask &= ~(ENABLE_SHOOT);

to clear a few flags:

my.emask &= ~(ENABLE_SHOOT|SOME_OTHER|ONE_MORE);

It's important to note that if the variable being manipulated is larger than an int, the value used in the 'and not' expression must be as well. Actually, one can sometimes get away with using smaller types, but there are enough odd cases that it's probably best to use type suffixes to make sure the constants are large enough.