Bit-Level vs Logical Operators in Computer Systems

1. CSC 2400: Computer SystemsBit-Level vs. Logical Operators

2. Review – Addition • 2’s complement addition is just binary addition • assume all integers have the same number of bits • for now, assume no overflow 01101000 (104) 11110110 (-10) + 11110000(-16) + (-9) 01011000 (88) (-19) Assume 8-bit 2’s complement numbers.

3. Review – Sign Extension • To add two numbers, we must represent them with the same number of bits. • If we just pad with zeroes on the left NOT GOOD!): • Instead, replicate the sign bit to the left: 4-bit8-bit 0100 (4)00000100 (still 4) 1100 (-4)00001100 (12, not -4; NOT GOOD!) 4-bit8-bit 0100 (4)00000100 (still 4) 1100 (-4)11111100 (still -4)

4. Review – Memory and Variables char c = ‘A’; char c = 65; char c = 0x41; int i = 258; int i = 0x102; int j = 0xF0A2;

5. Bit-Level OperatorsCommon to C and Java&, |, ~, ^, <<, >>

6. Bitwise Operators • Apply to any “integral” data type: long, int, short, char • View arguments as bit vectors • Arguments applied bit-wise

7. Bitwise Operators

8. NOT (~)Example

9. AND (&) and OR (I)and XOR (^) Examples

10. AND (&) and OR (I)and XOR (^) Examples 0x69 & 0x55 --> 0x______ 0x69 | 0x55 --> 0x______ 0x69 ^ 0x55 --> 0x______

11. Bitmasks • Used to change or query one or more bits in a variable • The bitmask indicates which bits are to be affected • Common operations: • Setting one or more bits to 1 • Setting one or more bits to 0 • Reading one or more bits

12. Bitmasks – set single bit to 1 • Assume that data is an integer variable (size is unknown) • Set the least significant bit of data to 1 (other bits are unchanged) • C statement: data | 1 data = _______________________;

13. Bitmasks – set multiple bits to 1 • Assume that data is an integer variable (size is unknown) • Set bit 0, 2 and 3 of data to 1 (leave the other bits unchanged): • C statement: data | 0xD data = _______________________;

14. Bitmasks – set byte to 0xFF • Assume that data is an integer variable (size is unknown) • Set the least significant byte of data to 0xFF • C statement: data | 0xFF data = _______________________;

15. Bitmasks – set another byte to 0xFF • Assume that data is an integer variable (size is unknown) • Set the 2nd least significant byte of data to 0xFF • C statement: data | 0xFF00 data = _______________________;

16. Bitmasks – clear (set to 0) single bit • Assume that data is an integer variable (size is unknown) • Set the least significant bit of data to 0: • C statement: data & ~1 data = _______________________;

17. Review – Common Bit Operations • Set one or more bits to 1 • Set one or more bits to 0 • Read one or more bits

18. Review – What Does This Code Do? int data = ...; data = data | 0x1; • Answer: • Set the least significant bit to 1

19. Review – What Does This Code Do? int data = ...; data = data | 0x4; bit 2 bit 1 bit 0 • Answer: • Set bit 2 (third least significant bit) to 1

20. Review – What Does This Code Do? int data = ...; data = data | 0xF; bit 3 bit 2 bit 1 bit 0 • Answer: • Set the four least significant bits to 1

21. Review – What Does This Code Do? int data = ...; data = data & ~0x1; bit 0 • Answer: • Clear the least significant bit (set it to 0)

22. Bitmasks – clear (set to 0) multiple bits • Assume that data is an integer variable (size is unknown) • Clear (set to 0) bits 0, 2 and 4 of data (other bits are unchanged): • C statement: data & ~0x15 data = _______________________;

23. Bitmasks – clear (set to 0) single byte • Assume that data is an integer variable (size is unknown) • Clear (set to 0) the least significant byte of data • C statement: data & ~0xFF data = _______________________;

24. Feedback Results • Review Topics (Today) • Ungraded Practice Quizzes (1/week) • Review Homework • More Hands-on/Labs/C Programming (Coming Up) • Teaching • Slow Down • Explain Jargon • Step-by-step Examples • When post slides?

25. Bitmasks – clear (set to 0) multiple bytes • Assume that data is an integer variable (size is unknown) • Clear (set to 0) bytes 0 and 1 of data • C statement: data & ~0xFFFF data = _______________________;

26. Bitmasks – read bit • Assume that data is an integer variable (size is unknown) • Determine the least significant bit of data: • C statement: data & 1 result = _______________________;

27. Bitmasks – read another bit • Assume that data is an integer variable (size is unknown) • Determine the 2nd least significant bit of data: • Need to shift

28. Bitwise Operator: Left Shift << • Left shift: A << n (same as multiply by 2n) • Shift the bit-vector A to the left by n bits • Leftmost n bits are lost; rightmost n bits become 0

29. Bitwise Operator: Right Shift >> • Right shift: A >> n (same as divide by 2n) • Shift the bit-vector A to the right by n bits • Rightmost n bits are lost; what about leftmost n bits? 1 1 1 0 0 0 • Uses sign extension for signed types

30. Bitwise Operator: Right Shift >> 0 0 0 0 0 0 • Insert 0 to the left for unsigned types Note: Java has the unsigned shift operator >>> (not available in C)

31. Bitmasks – revisit example • Determine the 2nd least significant bit of data (size unknown): • C statement: (data >> 1) & 1 result = _______________________;

32. Bitmasks – read another bit • Determine the 4nd least significant bit of data (size unknown): • C statement: (data >> 4) & 1 result = _______________________;

33. Bitmasks – read byte • Assume that data is an integer variable (size is unknown) • Determine the 2nd least significant byte of data • C statement: (data >> 8) & 0xFF result = _______________________;

34. Bitwise Operators • Write code to print all the bits of a character from left to right (starting with the most significant bit): char c = 0xB5; void print_binary(char c) { /* add code here */ } 1 0 1 1 0 1 0 1

35. Relations Between Operations • DeMorgan’s Laws • Express & in terms of |, and vice-versa • A & B = ~(~A | ~B) • A and B are true if and only if neither A nor B is false • A | B = ~(~A & ~B) • A or B are true if and only if A and B are not both false • Exclusive-Or using Inclusive Or • A ^ B = (~A & B) | (A & ~B) • Exactly one of A and B is true • A ^ B = (A | B) & ~(A & B) • Either A is true, or B is true, but not both

36. Why Bitwise Operators?

37. Used in Networking

38. Used in Encryption/ Decryption

39. Used in Compression • Look at the DEFLATE algorithm, for instance • https://en.wikipedia.org/wiki/DEFLATE • everything is bits, not bytes

40. Review – Bitwise Operators ~ & | ^ << >>

41. Contrast: Logical Operators

42. Logical Operators • Always return 0 or 1 • False is 0 in C • True is anything nonzero in C • Examples (char data type) • !0x41 --> _____ • !0x00 --> _____ • !!0x41 --> _____ • 0x69 && 0x55 --> _____ • 0x69 || 0x55 --> _____ && (Logical AND), || (Logical OR), ! (Logical NOT)

43. What is the Output? int a = 0x43, b = 0x21; printf("a | b = %x\n", a | b); _________ Printf("a || b = %x\n", a || b); ____1____ printf("a & b = %x\n", a & b); _________ printf("a && b = %x\n", a && b); ____1____

44. Mental Exercise /* * isNotEqual - return 0 if x == y, and 1 otherwise * Examples: isNotEqual(5,5) = 0, isNotEqual(4,5) = 1 */ intisNotEqual (int x, int y) { return ______________; }

45. What did we learn? • Bit-level operators (&, |, ~, ^, <<, >>) • Operate on bits (view arguments as bit vectors) • Logical operators (&&, ||, !) • Always return 0 (False) or 1 (True)

46. Midterm Review Topics • Number Representations and Casting/Conversion: • Binary, Hexadecimal, Octal, Little and big endian, sign extension • Signed Magnitude, 1’s Complement, 2’s Complement • IEEE 32-bit and 64-bit Floating Point, ASCII • Addition in different representations, overflow, limits of representation • Bitwise and Logical Operators: AND, OR, NOT, XOR, L&R SHIFT • Unix Commands: ls, cd, mkdir, cp, mv, rm, chmod, pwd, -r, etc • Absolute and Relative Paths, permissions, navigating directory structure • C programming and differences with Java • Computer Systems (hw/sw, analog/digital), Data Sizes, etc • Sources: ZyBook, Tarnoff, Slides, Labs and Homework • Problems: Short Answer, MC, True False, and Problem Solving