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Bitwise Operations

Bitwise Operations. CSE 2451 Matt Boggus. 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; Hexidecimal (2 4 or 4 bits) Starts with 0x Valid digits: 0-9 and A-F int y = 0xFF12;

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Bitwise Operations

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  1. Bitwise Operations CSE 2451 Matt Boggus

  2. 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; • Hexidecimal(24or 4 bits) • Starts with 0x • Valid digits: 0-9 and A-F • int y = 0xFF12; • Octal (23or 3 bits) • Starts with 0 • Valid digits: 0-7 • int w = 067; • Binary (21or 1 bit) • Starts with 0b • Valid digits: 0,1 • int z = 0b01001;

  3. 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

  4. 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

  5. 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)

  6. Examples (assuming an int is only 8-bits) intc, 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 stdlinux a is 240 b is 170

  7. AND and OR usage: bit masking

  8. 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

  9. 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

  10. 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 right copy = copy >> 1; }

  11. Code example Output is: a is f0f0 b is 5555 a >> 4 is f0f b >> 4 is 555 binary = 42 #include <stdio.h> void main() { unsigned inta,b,c,d,e; a = 0xF0F0; b = 0x5555; c = a >> 4; d = b >> 4; e = 0b01000010; // %x is unsigned int in hex printf("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); } Note: printf does not directly support printing values in binary or octal form, only decimal and hex

  12. 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 */

  13. 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

  14. Additional (non-bitwise) operators

  15. Conditional Operator – If/Then/Else • Ternary operator ? : • Syntax bool ? exp1 : exp2 • Evaluation • If bool is true (non-zero), the result is exp1 • If boolis 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))

  16. 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 15 value= (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!= ‘10’) • Usually result in code that is less readable

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