Bitwise Operations

CSE 2451Rong Shi

Working with bits – int values• Decimal (not a power of two – used for human readability)

– No preceding label– Valid digits: 0-9– int x = 22;

• Hexadecimal (24 or 4 bits)

– Starts with 0x– Valid digits: 0-9 and A-F– int y = 0xFF12;

• Octal (23 or 3 bits)

– Starts with 0– Valid digits: 0-7– int w = 067;

• Binary (21 or 1 bit)

– Starts with 0b– Valid digits: 0,1– int z = 0b01001;

Bitwise Operations

• Operate on the bits of a data word

• Corresponding bits of both operands are combined by the usual logic operations

• Apply to integer types, not floats

Why use bitwise operators?

• Cryptography• Compression algorithms• Computer graphics• Embedded devices and data storage efficiency• Hash functions• Network protocols• Not necessarily faster than arithmetic operations– Some nifty tricks though

Bitwise operators& AND Result is 1 if both operand bits are 1

| OR Result is 1 if either operand bit is 1

^ Exclusive OR Result is 1 if operand bits are different

~ One’s Complement Each bit is reversed

<< Shift left Move every bit left (multiply by 2)

>> Shift right Move every bit right (divide by 2)

Examples (assuming an int is only 8-bits)

int c, a, b;a = 0b11110000;b = 0b10101010;c = a & b; // 1010 0000 c = a | b; // 1111 1010 c = a ^ b; // 0101 1010 c = ~a; // 0000 1111 c = a << 2; // 1100 0000 c = a >> 5; // 0000 0111

What are a and b’s decimal values?

Depends on if the leftmost or rightmost is the most significant bit. On stdlinuxa is 240b is 170

AND and OR usage: bit masking

XOR usage: swapping

temp = x;x = y;y = temp;

x = x ^ y;y = x ^ y;x = x ^ y;

Additional XOR uses and a proof for the validity of

swapping

Bit shifts and overflows

• Shift k bits : multiply or divide by 2k

– New bits “shifted in” are zeroes• Some bit shifts are poorly defined, their

results are implementation dependent– a << -5– a << 493

Looping using bitwise operations

int copy = n;while (copy != 0){

// …do stuff with copy…// how would you “access” the least significant bit?

// move every bit rightcopy = copy >> 1;

}

Code example#include <stdio.h>void main() {

unsigned int a,b,c,d,e;a = 0xF0F0;b = 0x5555;c = a >> 4;d = b >> 4;e = 0b01000010;// %x is unsigned int in hexprintf("a is %x\n",a);printf("b is %x\n",b);printf("a >> 4 is %x\n",c);printf("b >> 4 is %x\n",d);printf("binary = %x\n",e);

}

Output is:a is f0f0b is 5555a >> 4 is f0fb >> 4 is 555binary = 42

Note: printf does not directly support printing values in binary or octal form, only decimal and hex

Traditional Bit Definition#define EMPTY 01 #define JAM 02 #define LOW_INK 16 #define CLEAN 64 char status;

Example statements:if (status == (EMPTY | JAM)) ...; if (status == EMPTY || status == JAM) ...; while (! status & LOW_INK) ...; int flags |= CLEAN /* turns on CLEAN bit */ int flags &= ~JAM /* turns off JAM bit */

Traditional Bit Definitions

• Used very widely in C – Including a lot of existing code

• No checking – You are on your own to be sure the right bits are set

• Machine dependent – Need to know bit order in bytes (8 bits), byte order in

words (2, 4, … bytes)• Working with individual bits– Use AND and shift to extract– Use shift and OR to insert

Additional (non-bitwise) operators

Conditional Operator – If/Then/Else

• Ternary operator ? :• Syntax bool ? exp1 : exp2 • Evaluation

– If bool is true (non-zero), the result is exp1– If bool is false (zero), the result is exp2

• Example:int a = 10;int b = 20;x = a > b ? a : b; // x = b since a is less than b

• Style– Rarely more readable than using if/else– Useful in macros – ex: #define MAX(a, b) (((a)>(b)) ? (a) : (b))

Comma operator (when used in arithmetic expressions)

• Syntax exp1, exp2, exp3, …, expn• Evaluate statements from left to right, result of the entire expression

is expn (rightmost exp)• Example:

// x is set to 10, y is set to 5, and value is set to 15value = (x = 10, y = 5, x + y);

• Comma operator has lowest precedence – use parenthesis• Style

– Rarely more readable than using multiple single expressions– Can be used to cause “side effects”

• Side effect – a statement that modifies a variable or program state in addition to returning a value

• Ex: while (c=getchar(), c!= ‘9’)• Usually result in code that is less readable