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 (2 4 or 4 bits) – Starts with 0x – Valid digits: 0-9 and A-F – int y = 0xFF12; Octal (2 3 or 3 bits) – Starts with 0 – Valid digits: 0-7 – int w = 067; Binary (2 1 or 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 Some nifty tricks though

5. Bitwise operators & ANDResult is 1 if both operand bits are 1 | ORResult is 1 if either operand bit is 1 ^ Exclusive ORResult is 1 if operand bits are different ~One’s Complement Each bit is reversed <<Shift leftMove every bit left (multiply by 2) >>Shift right Move every bit right (divide by 2)

6. 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 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 2 k – 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 #include 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 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); } Output is: a is f0f0 b is 5555 a >> 4 is f0f b >> 4 is 555 binary = 42 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? : Syntaxbool ? 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))

16. Comma operator (when used in arithmetic expressions) Syntaxexp1, 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