Page 217 - Introduction to Microcontrollers Architecture, Programming, and Interfacing of The Motorola 68HC12

194 Chapter 7 Arithmetic Operations

to evaluate the formula from its tree representation will be virtually the same one that we
use to scan that tree from the left in Chapter 10. Any operation with two operands, such
as +, has a tree with two branches and nodes whose values are the operands for the
operation. For example, the result of x + y and x * y are represented by the trees

If the operation has only one operand, the operation is displayed as a tree with only
one branch. For example, sin(y) and sqrt(x) (for "square root of x") have trees

If your formula is more complicated than those shown above, you just plug in the
results of one tree where the operand appears in the other tree. For instance, if you want
the tree for sqrt(x + y), just substitute the tree for x + y into the node, for example,

The tree for the formula (8) is shown in Figure 7.12. Notice how the formula is like
a projection onto a horizontal line below the tree and how the tree can be built up from
the bottom following the "plug in" technique just described.

Figure 7.12. Finding a Parsing Tree for (8) from the Bottom Up