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Arithmetic Expressions
ã (a + b) * (c + d) + e – f/g*h + 3.25 ã Expressions comprise three kinds of entities.
– Operators (+, - / *) (+ -, /, ). – Operands (a, b, c, d, e, f, g, h, 3.25, (a + b), (c + d), etc.). d) etc ) – Delimiters ((, )).
Evaluation of Expressions
Operator Degree
ã Number of operands that the operator requires. i ã Binary operator requires two operands. y p q p
–a+b –c/d –e-f
Infix Form
ã Normal way to write an expression. ã Binary operators come in between their left and

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Evaluation of Expressions
ã(a + b) * (c + d) + e
–
f/g*h + 3.25ãExpressions comprise three kinds of entities.
* – ,-, , .
–Operands (a,b,c,d,e,f ,g,h,3.25,(a + b),(c +
,.. –Delimiters ((,)).
ãNumber of operands that the operator requres.ãBinary operator requires two operands.
–a + b –c/d
–e -f
.
–+ g –-
ãNormal way to write an expression.ãBinary operators comeinbetween their left.
–a * b –a + c –a * b / c –(a + b) * (c + d) + e
–
f/g*h + 3.25
ãHow do you figure out the operands of anoperaor
–a + b * c –a * b + c / d
ãThisisdonebassininoerator priorities.
–*=>=-
ãWhen an operand lies between two,operator that has higher priority.
++
ãWhen evaluating
Priority Operator
1
Unary minus, !
same priorities, it
2
*, /, %
from left to right.
, -
4
<, <=, >=, >
ã
–Nonzero as true
5
==(equal), !=
6
&&and –zero as false –!3&&5 +1
0
7
||(or)
ãx=6, y=5ã+*+
ã(x>=5)&&y<10ã!x>10+!y
ãWhen an operand lies between twooperators that have the same priority, theoerand associates with the oerator onthe left.
–- –a * b / c / d
Delimiters
ãSubexpression within delimiters istreated as a single operand,indeendent from the remainder of theexpression.
* –
–
–
ãNeed operator priorities, tie breaker,an emers.ãThis makes computer evaluation more
difficult than is necessary.ã not rely on operator priorities, a tie, .ãSo it is easier for a computer toforms.
constant is the same as its infix form.
–a,b,3.25
ãsame in infix and postfix forms.ãperaors come mmeaeyaer epostfix form of their operands.
–Infix= a + b –=
ãInfix =a + b * c
–Postfix=
abc*+
ãInfix =a * b + c
Postfix =ab*c+
ãInfix =
(a + b) * (c –d) / (e + f)
Postfix =ab+cd-*ef+/
ãReplace with new symbols.
–+ a => a @ –++=>+ –-a => a ? –-a- = a -
Expressions are converted into Postfix notation before.X = A / B –C + D * E –A * CInfix=> A / B –C + D * E –A * CPostfix => A B / C –D E * + A C * -
(Operators come in-between operands)(Operators come after operands)
OperationPostfixT
1
= A / BT
1
C –D E * + A C * -T
2
= T
1
-CT
2
D E * + A C * -T
3
= D * ET
2
T
3
+ A C * -T
4
= T
2
+ T
3
T
4
A C * -T
5
= A * CT
4
T
5
-T
6
= T
4
-T
5
T
6
ãScan postfix expression from left to rightpusng operans on o a sac.ãWhen an operator is encountered, popas many operands as this operator needs; evaluate the oerator; ush theresult on to the stack.ã , ,operators come immediately after their .
ã(a + b) * (c
–
d) / (e + f)ãa b + c d -* e f + /*-
ãa b+ c d -* e f + / ãa b +c d -* e f + / astack

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