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order of precedence
summary
This subchapter looks at order of precedence.
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This subchapter looks at order of precedence.
free computer programming text book projecttable of contents

This subchapter looks at order of precedence.
Every programming language needs to have some system for determining the order of evaluation of expressions.
x := 5 + 6 * 7;
or
x = 5 + 6 * 7
Is x 47 or 77?
(5 + 6) = 11; followed by 11 * 7 = 77
(6 * 7) = 42; 5 + 42 = 47
The normal rules of elementary algebra call for multiplication (and division) to have a higher priority than addition (or subtraction), which would make x = 42.
elementary algebra 

parenthesis 
exponentiation 
multiplication 
division 
addition 
subtraction 
A strict left to right evaluation would make the answer x = 77.
A strict right to left evaluation would make the answer x = 42.
The use of a reverse Polish notation (RPN, such as is used in Forth) avoids the question.
The two most common approaches used in computer programming languages are either (1) some order of precendence) or (2) directional evaluation (lefttoright or righttoleft).
The use of parenthesis can be used to change the normal order of evaluation.
Parenthesis can also be used to make complicated expressions more clear to a human reader. This makes the program easier to udnerstand and easier to maintain over years or decades of use.
The order of precedence in the following charts are from highest to lowest (top to bottom). Items on the same level are of equal order of precendence.
Primaryexpression operators  

15  ( ) [ ] . > 
Unary operators  
14  * &  ! ~ ++  sizeof (type) 
13  * / % 
12  +  
11  >> << 
10  < > <= >= 
9  == != 
8  & 
7  ^ 
6   
5  && 
4   
3  ?: 
Assignment operators  
2  = += = *= /= %=
>> =< <= &= ^= = 
Sequence operator  
1  , (comma) 
unary + unary  not 
* / div mod and 
+  or 
= <> < <= > >= in 
1  all subexpressions in parenthesis from innermost to outermost 
2  all exponentiations from right to left 
3  all multiplications and divisions from left to right 
4  all additions and subtractions from left to right 
1  parenthesis 
2  ↑ (exponentiation) 
3  × / ÷ (multiplication and division) 
4  +  (addition and subtraction) 
5  < ≤ = ≠ ≥ > (relational operators) 
6  ¬ (not) 
7  ∧ (and) 
8  ∨ (or) 
9  ⊃ (implies) 
10  ≡ (is equivalent to) 
Note that the actual ALGOL symbol for is not greater than has the less than symbol over the equals symbol rather than ≤ and the ALGOL symbol for not less than has the greater than symbol over the equals symbol rather than ≥.
The following material is from the unclassified Computer Programming Manual for the JOVIAL (J73) Language, RADCTR81143, Final Technical Report of June 1981.
1.1.3 Calculations
In the simplest case, calculations is performed by an assignment
statement. An example is:
AVERAGE = (X1 + X2)/2;
The righthandside of this assigment is a formula; it forms the
sum of X1 and X2 and divides it by 2. The details of the
operation depend on how X1 and X2 are declared. If X1 and X2 are
declared float, the calculation is very likely to produce the
expected result. In contrast, if the X1 and X2 are declared
fixed, the scaling must be worked out by the programmer to make
sure the calculation will succeed. And if X1 and X2 are declared
characterstring, the compiler will reject it because JOVIAL does
not automatically convert values into the types required by
operators.
In the example just given, the parenthesis show that the addition
is performed before the division. When parenthesis are not
given, JOVIAL recognizes the usual order of evaluation. Here is
an example:
POLY = BETA*X1**2  GAMMA*X2 + DELTA;
JOVIAL applies its "rules of precedence" to the formula in this
assignment and thus interprets it as:
POLY = (((BETA*(X1**2))  (GAMMA*X2)) + DELTA);
The complete precedence rules are given in Chapter 11.
Chapter 1 Introduction, page 6
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