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Extra resources for C++ Programming for Game Developers, Module II (Textbook)

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The same logic can be made for 32-bit numbers, 64bit numbers, and so on. We now see where those type ranges come from. Clearly, the more bits we use, the more kinds of numbers we can represent. 3. Five bit operations exist: a. A bitwise AND written as A & B, which for each corresponding bit in A and B, returns a “true” bit if the bits are both “true”, otherwise it returns a “false” bit. b. A bitwise OR written as A | B, which for each corresponding bit in A and B, returns a “true” bit if at least one of the bits is “true,” otherwise it returns a “false” bit.

1 Counting in Hexadecimal The hexadecimal (hex for short) number system is a base sixteen number system. This means that sixteen possible values per digit exists; namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Notice that we must add new symbols to stand for the values above 9 that can be placed in a single digit; that is, A = 1010 , B = 1110 , C = 1210 , D = 1310 , E = 1410 , F = 1510 . As we did in binary, let us count a few numbers one-by-one to get a feel for hex. For each number, we write the equivalent decimal and binary number next to it.

Here is an example: unsigned char A = 0xB9; unsigned char B = 0x91; unsigned char C = A & B; // AND the bits and store the result in C. To see what is happening, let us look at the binary: A = 1011 1001 B = 1001 0001 1011 1001 & 1001 0001 ----------C = 1001 0001 So, what we do is match each corresponding bit in A and B together, and if both bits are set, then the corresponding bit in C is set. If both bits are not set, then the corresponding bit in C is not set. As you can see, only the first bit, fifth bit, and eighth bit are both on in A and B, and thus those are the only bits set in C.

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