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

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So we write one in the first column: 101 - 11 -----0 In the second column, we must borrow again yielding: 10 001 - 11 -----10 Example 6: 10110 101 -------? Here the first column must borrow, and then 10 – 1 = 1: 10 10100 101 -------1 In the second column we now have 0 – 0 = 0, in the third column we have 1 – 1 = 0, in the fourth column we have 0 – 0 = 0, and in the fifth column we have 1 – 0 = 1, which gives the answer: 10 10100 101 -------10001 42 Multiplication Multiplying in binary is the same as in decimal; except all of our products have only four possible forms: 0 × 0 , 0 × 1 , 1× 0 , and 1× 1 .

1111 x 11 ------? 10101 x 110 -------? 11001101 + 1 ---------? 2 Hex Arithmetic Perform the following hex arithmetic operations. Use a calculator, such as the Windows calculator program, to check your work. AAA + 555 -----? BB + A4 ----? FEDCA + 1234 ------? 12FE5BA + 45AFCD --------? 57 AAA - 555 -----? BB - A4 ----? FEDCA - 1234 ------? 12FE5BA - 45AFCD --------? AAA x 5 -----? BB x A4 -----? FEDCA x A ------? 12FE5BA x CF --------? 3 Base Conversions For the following conversions, use a calculator, such as the Windows calculator program, to check your work.

One of the reasons we like to work in hex is because we can mentally “visualize” the binary digit layout in hex just as clearly as seeing the actual binary number. In addition, hex has the nice property of being able to describe the same number with a smaller number of digits. That is, big numbers in binary take a lot of digits to describe, so from that standpoint, hex is much more compact. 4 Converting Binary to Hexadecimal Converting from binary to hex is equally easy. Consider the number 111010111110111000 2 .

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