5. Arithmetic Operations.
a. General. Now that you know how to count and convert, the next step is to perform addition and
subtraction in nondecimal numbering systems. To understand how the computer computes, you must
understand these mathematical operations and how to perform them. The first task is to learn the machine
methods of performing arithmetic computations. Knowledge of how the computer is designed is not
required to use these methods. Although this chapter introduces some computer terminology and theory,
the primary concern is with pencil and paper solutions that result when you use the same methods that
computers use.
b. Rules for Addition. The rules taught in elementary school for adding decimal numbers can be
used in adding numbers in any system. The only differences are the breakpoints in the nondecimal
systems. The counting and breakpoint for carrying is the important operation. In the following
descriptions of addition, we will emphasize the binary system.
(1) The rules of binary addition are simple because of the small radix. The rules differ from
regular decimal addition only when the radix or breakpoint is reached.
(a) Adding 0 and 0 yields 0:
(b) Adding 0 and 1 or 1 and 0 yields 1:
(c) Adding 1 and 1 yields 0 with a carry of 1. This rule shows the point at which the radix of
the binary system is reached:
(2) Single addition. Using the rules for adding binary numbers, the following are examples of
how to add and how to check the results in the decimal system.
(a) In this example, adding 0 and 1 yields 1; adding 1 and 0 yields 1. This gives the correct
answer of 11 (note that the least significant digit is to the right). The check in decimal numbers yields an
answer of 3 which equals binary 11.
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