Introduction to computer systems architecture and programming

168 Introduction to computer systems architecture and programming
XOR operator
A (input) B (input) C (output)
TRUE TRUE FALSE
TRUE FALSE TRUE
FALSE TRUE TRUE
FALSE FALSE FALSE
Table 2.3: The Boolean operation XOR.
NOT operator
A (input)
C (output)
TRUE
FALSE
FALSE
TRUE
Table 2.4: The Boolean operation NOT.
Note: You can also think of A and B as statements that can be TRUE or
FALSE. For example, A could be the TRUE statement ‘5 > 3’. However,
these statements may also contain variables, e.g. B might be the statement
‘X is a prime number’ which is TRUE or FALSE depending on the value of
X. You will use these kinds of statements in some of your programming
techniques later.
Let us now consider the gate again. A gate has one or more inputs and
produces exactly one output. Input and output can be at one of two
different voltage levels, which in turn represent 1 and 0 (or TRUE and
FALSE). In this way logic gates can perform logical operations; that is, you
can think of them as boxes which receive multiple inputs and produce one
output according to the truth tables above (Brookshear 2009). Figure 2.1
gives you the standard gate representations for the Boolean operations
introduced in this chapter.
inputs
NOT
output
inputs
AND
output
inputs
OR
output
inputs
XOR
output
Figure 2.1: Gate symbols for Boolean operators.
Several gates (i.e. permutations of NOT, AND, OR, XOR) can then be
arranged to create circuits that can perform logical and also arithmetic
operations like adding two numbers. For example, if we combine an XOR
gate with an AND gate as shown below, we get what is referred to as a
half adder. The half adder adds the two binary digits A and B. Different
combinations of inputs A and B result in the sum of inputs A and B and the
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