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Bitwise Operations

This guide provides a comprehensive overview of bitwise operations in C programming. Covering integer data types, we explore the binary, decimal, hexadecimal, and octal representations, as well as the significance of bitwise operators like AND, OR, XOR, and shifts. You'll learn where these operations are useful and how they apply to areas such as cryptography and network protocols. Additionally, practical examples illustrate typical use cases, including bit manipulation techniques for effective data handling. Perfect for newcomers and those refining their skills in low-level programming.

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Bitwise Operations

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  1. Bitwise Operations CSE 2451 Rong Shi

  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; • Hexadecimal (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!= ‘9’) • Usually result in code that is less readable

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