C/C++ Bitwise operations

The most fundamental operations of the computer are:

AND OR NOT moving data

All other operations (including Exclusive OR (XOR) are built on these.

Binary Operations take two pieces of data of the same size and compare them bit-by-bit, i.e., compare the right-most (least significant) bit of the first data piece with the least significant bit of the second data piece, and so on through the most significant bit of each.

AND ( & )

The AND operation, represented in C++ as  &  , checks to see if the corresponding bits are BOTH set to 1.  If they are, the answer bit is set to 1; if not, the answer bit is set to 0. For example:
  char a = '\05', b = '\03';
would give us, in binary,

	a	=	00000101	(5)
	b	=	00000011	(3)
	a & b	=	00000001	(1)

since the only bit that is set to 1 in both a AND b is the right-most (least significant) bit.
Both a and b remain unchanged.

OR ( | )

The OR operation, represented in C++ as  |  , checks to see if either of the corresponding bits are set to 1.  If one, the other or both are, the answer bit is set to 1; if not, the answer bit is set to 0. For example:
  char a = '\05', b = '\03';
would give us, in binary,

	a	=	00000101	(5)
	b	=	00000011	(3)
	a | b	=	00000111	(7)

since the three right-most (least significant) bits are set to 1 in one, the other OR both a and b .
Both a and b remain unchanged.

 

XOR (^)

The Exclusive OR (XOR) operation, represented in C++ as  ^ , checks to see if the corresponding bits are set to different values.  If one or the other but not both are set to 1, the answer bit is set to 1; if not, the answer bit is set to 0; i.e., a ^ b = (a | b) & ~(a & b) . For example:
  char a = '\05', b = '\03';
would give us, in binary,

	a	=	00000101	(5)
	b	=	00000011	(3)
	a | b	=	00000110	(6)

since the three right-most (least significant) bits are set to 1 in one, the other but not both a and b .
Both a and b remain unchanged.

Unary Operations look at one piece of data, evaluating it on the value of each individual bit.

NOT ( ~ )

The NOT operation, also called One's Complement, is represented in C++ as  ~  . It checks to see if each bit is set to 1 or 0.  If the bit is set to 0, the answer bit is set to 1; if the bit is set to 1, the answer bit is set to 0. For example:
  char a = '\05';
would give us, in binary,

	a	=	00000101	(5)
	~a	=	11111010	(250)

since the only bit that is set to 1 in both a AND b is the right-most (least significant) bit.
a remains unchanged.

Moving Data:

Left-Shift ( << )

The Left-Shift operation, represented in C++ as  <<  ,  moves bits in the answer a specified number places to the left, bringing zeros in on the right. For example:
  char a = '\05';
would give us, in binary,

	a	=	00000101	(5)
	a << 2	=	00010100	(20)

giving the "101" pattern moved two places to the left, with zeros in the last two places.
a remains unchanged.

Right-Shift ( >> )

The Right-Shift operation, represented in C++ as  >>  ,  moves bits in the answer a specified number places to the right, bringing zeros in on the left. For example:
  char a = '\05';
would give us, in binary,

	a	=	00000101	(5)
	a >> 2	=	00000001	(1)

giving the "101" pattern moved two places to the right (dropping off the last two digits), with zeros in the first two places.
a remains unchanged.

All of these operators have accompanying assignment operators: &=, |=, ~=, ^=, <<=, >>=.

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