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## Chapter 8. Binary Arithmetic

### Before We Start ….

Because digital computers are constructed from logic gates that can represent only two states, they are obliged to make use of the binary (base-2) number system with its two digits: 0 and 1 (see Chapter 7: Alternative Numbering Systems, for more details on binary).

Unlike calculations on paper where both decimal and binary numbers can be of any size—limited only by the size of your paper, the endurance of your pencil, and your stamina—the numbers manipulated within a computer have to be mapped onto a physical system of logic gates and wires. Thus, the maximum value of a number inside a computer is dictated by the width of its data path; that is, the number of bits used to represent that number. ...

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