Expressions and Precedence - faculty-web.msoe.edu filePrecedence Operator Description Associativity 1 ++ -- Suffix/postfix increment and decrement Left -to right Function call [] Array

Expressions and Precedence

Last updated 12/11/19

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• Expression: Sequence of Operators and Operands that reduce to a single value

• Simple and Complex Expressions

• Subject to Precedence and Associativity

• Six categories• Primary• Postfix• Prefix• Unary• Binary• Ternary

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• Simple Expressions

• Only 1 operator

• a + b

• Complex Expressions

• Multiple operators

• 2*3/6

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• Primary Expressions

• One operand and no operators

• Namea interest_rate RATE initial1

• Literal2 123.456 ‘a’ “hello ee1910”

• ParentheticalAnything in parentheses reduces to a single value

(2 + 3 * 4) (a = b + c)

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• Postfix Expressions

• One operand followed by one operator• Operand must be a variable

• Function CallFunction name is an operand (named entity)

Parenthesis are the operator

printf(…)

• Postfix increment/decrementi++ → i = i + 1

j-- → j = j - 1

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• Postfix Expressions

• Some expressions have a Value and a Side Effect

int j;

int x;

j = 5;

x = j++;

Value: x = 5

Side Effect: j = 6

• Postfix indicates to operate after the evaluation

Consider printf(“%d”, j++);

5 or 6 ?

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• Prefix Expressions

• One operator followed by one operand• Operand must be a variable

• Only 2 examples

• Prefix increment/decrement++j → j = j + 1

--k → k= k - 1

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• Prefix Expressions

• Some expressions have a Value and a Side Effect

int j;

int x;

j = 5;

x = ++j;

Value: x = 6

Side Effect: j = 6

• Prefix indicates to operate before the evaluation

Consider printf(“%d”, ++j);

5 or 6 ?

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• Unary Expressions

• One operator followed by one operand• Operand can be any expression

+, -

cast

sizeof(int). …

a = 5

+a -> +5 Note: the expression is modified

-a -> -5 not the variable, a = 5 in both cases

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• Binary Expressions

• Operand operator operand• Familiar to us: +, -, *, /

• New: % - modulus (remainder of a division)

• Subject to type limitations

10 * 2 → 20 10 / 2 → 5

true * 2 → 2 true / 2 → 0 ???

‘A’ * 2 → 130 ‘A’ / 2 → 32 ???

15.6 * 2 → 31.2 15.6 / 2 → 7.8

3 / 5 → 0 12 / 5 → 2

3 % 5 → 3 12 % 5 → 2

Modulo only operates on integers

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• Binary Expressions

• Special binary expression - assignment• variable = expression• Has both a value - result of right side• And a side effect – places value into the variable on the left

side

• Simplea = b + c j = j * 2

• Compound*=, /=, +=, -=, %=a *= b → a = a * ba += 10 → a = a + 10a -= b + c → a = a – (b + c) expression is evaluated first

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• Ternary Expressions

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• Precedence

• Order in which operators are evaluated• In math: * and / before + and –

• 2/3+3*4 → ((2/3) + (3*4))

• Associativity

• Order in which operators with the same precedence are evaluated• In math: left to right

• 2 + 3 – 4 + 5 → (((2 + 3) – 4) + 5)

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Precedence Operator Description Associativity

1

++ -- Suffix/postfix increment and decrement Left-to-right

() Function call

[] Array subscripting

. Structure and union member access

-> Structure and union member access through pointer

(type){list} Compound literal(C99)

2

++ -- Prefix increment and decrement Right-to-left

+ - Unary plus and minus

! ~ Logical NOT and bitwise NOT

(type) Type cast

* Indirection (dereference)

& Address-of

sizeof Size-of

_Alignof Alignment requirement(C11)


1


() Function call





2




(type) Type cast


& Address-of

sizeof Size-of


3 * / % Multiplication, division, and remainder Left-to-right

4 + - Addition and subtraction

5 << >> Bitwise left shift and right shift

6< <= For relational operators < and ≤ respectively

> >= For relational operators > and ≥ respectively

7 == != For relational = and ≠ respectively

8 & Bitwise AND

9 ^ Bitwise XOR (exclusive or)

10 | Bitwise OR (inclusive or)

11 && Logical AND

12 || Logical OR

13 ?: Ternary conditional Right-to-Left

14

= Simple assignment

+= -= Assignment by sum and difference

*= /= %= Assignment by product, quotient, and remainder

<<= >>= Assignment by bitwise left shift and right shift

&= ^= |= Assignment by bitwise AND, XOR, and OR

15 , Comma Left-to-right

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1


() Function call





2




(type) Type cast


& Address-of

sizeof Size-of



1


() Function call





2




(type) Type cast


& Address-of

sizeof Size-of


3 * / % Multiplication, division, and remainder Left-to-right

4 + - Addition and subtraction

5 << >> Bitwise left shift and right shift

6< <= For relational operators < and ≤ respectively

> >= For relational operators > and ≥ respectively

7 == != For relational = and ≠ respectively

8 & Bitwise AND

9 ^ Bitwise XOR (exclusive or)

10 | Bitwise OR (inclusive or)

11 && Logical AND

12 || Logical OR

13 ?: Ternary conditional Right-to-Left

14

= Simple assignment

+= -= Assignment by sum and difference

*= /= %= Assignment by product, quotient, and remainder

<<= >>= Assignment by bitwise left shift and right shift

&= ^= |= Assignment by bitwise AND, XOR, and OR

15 , Comma Left-to-right

* & and () have multiple definitionsUsage is context dependent

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• Examples (ints)

a = 2, b=3, c=4

1 + 2 * 3 →

1 + 2 * 3 / 2 →

-b++ →

a += b *= c -= 3 →

--a * (1 + b) / 3 – c++ * b →

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• Examples

a = 2, b=3, c=41 + 2 * 3 → 1 + (2 * 3) = 71 + 2 * 3 / 2→ 1 + ((2 *3) /2) = 1 + (6/2) = 4

same precedence (L-R)-b++ → -(b++) = -3 evaluates first (b is now 4)a += b *= c -= 3 → c= 1, b=3, a=5 same precedence (R-L)

--a * (1 + b) / 3 – c++ * b →

--a * 4 / 3 – c++ * b --a * 4 / 3 – 4 * b1 * 4 / 3 – 4 * b4 / 3 – 4 *31 - 12-11 Answers

Answers

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• Precedence and Associativity

For clarity and precision

Use Parenthesis freely

(((--a) * (1 + b) )/ 3) – ((c++) * b) →

((( 1 ) * ( 4 )) / 3 ) – (( 4 ) * 3 )(( 4 / 3 ) – ( 12 ))( 1 – 12 )-11

a = 2, b=3, c=4

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Number Systems

• Special note on binary numbers in C programming

• Some but not all compilers allow binary numbers to be represented in C code directly

95 → 0b01011101

• To be safe and ensure our code is portables we will NOTuse this notation.

• Binary numbers can be represented with:• Their decimal equivalents 95

• Their hexadecimal equivalents 0x5D

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• Bitwise Operatorsa = 0x86, b = 0xA5, c = -35 (8 bit values)

• ~ bitwise not• inverts the individual bits in a number• ~a→ ~(1000 0110) → 0111 1001 → 0x79• ~c→ ~(1101 1101) → 0010 0010 → 34

• | bitwise or• ORs the individual bits• a | b → (1000 0110) | (1010 0101) → 1010 0111 → 0xA7

• & bitwise and• ANDs the individual bits• a & b → (1000 0110) & (1010 0101) → 1000 0100 → 0x84

• ^ bitwise xor• XORs the individual bits• a ^ b → (1000 0110) ^ (1010 0101) → 0010 0011 → 0x23

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• Bitwise Operatorsuint8_t a;

int8_t b;

a = 0xA6;

b = 0xA6;

• >> bitwise shift right• shifts the individual bits in a number to the right

• a >> 2 → (1010 0110) >> 2 → 0010 1001 - unsigned

OR

• b >> 2 → (1010 0110) >> 2 → 1110 1001 - signed

• << bitwise shift left• shifts the individual bits in a number to the left

• a << 3 → (1010 0110) << 3 → 0011 0000 - unsigned or signed

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• Logical Operators

• ! logical not• inverts the logical value• !true → false• !34 → false

• || logical OR• evaluates both sides logically then does an OR• true || false → true• 0 || 0 → false• 34 || -32 → true

• && logical AND• evaluates both sides logically then does an AND• true && true → true• 1 && 0 → false• 34 && -32 → true

Reminder: The ONLY integer valuethat is false is 0

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• Relational Operators

• ==, <, >, <=, >=, !=• equals, LT, GT, LE, GE, not equal

• evaluates by type

• evaluates to Boolean T or F

• true == true → true

• 34 == 32 → false

• 34 != 32 → true

• 5 >= 5 → true

• 3.5 <= 12 → true

• true < 5 → true

• true == -15 → true

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Expressions and Precedence - faculty-web.msoe.edu filePrecedence Operator Description Associativity 1 ++ -- Suffix/postfix increment and decrement Left -to right Function call [] Array