CSC 2400: Computer Systems Bit-Level vs. Logical Operators Review - - PowerPoint PPT Presentation

CSC 2400: Computer Systems

Bit-Level vs. Logical Operators

Review – Addition

q 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.

Review – Sign Extension

q To add two numbers, we must represent them with the

same number of bits.

q If we just pad with zeroes on the left NOT GOOD!): q Instead, replicate the sign bit to the left:

4-bit 8-bit 0100 (4) 00000100 (still 4) 1100 (-4) 00001100 (12, not -4; NOT GOOD!) 4-bit 8-bit 0100 (4) 00000100 (still 4) 1100 (-4) 11111100 (still -4)

Review – Memory and Variables

int i = 258; 00000000 00000000 00000001 00000010 int i = 0x102; 00000000 00000000 00000001 00000010 01000001 char c = ‘A’; 01000001 char c = 65; 01000001 char c = 0x41; int j = 0xF0A2; 00000000 00000000 11110000 10010010

Bit-Level Operators

Common to C and Java &, |, ~, ^, <<, >>

Bitwise Operators

~ Bitwise NOT “flips” bits & Bitwise AND 1 if both operands are 1 | Bitwise OR 0 if both operands are 0 ^ Bitwise XOR 0 if operands are equal << Bitwise Left Shift shifts bits to the left >> Bitwise Right Shift shifts bits to the right

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

Bitwise Operators

A B ~A A&B A|B A^B A^A 1 1 1 1

NOT (~) Example

Input 1 1 1 1 0xB4 ~Input 0x___

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

A 1 1 1 1 0xB4 B 1 1 1 1 1 0x___ A & B 0x___ A | B 0x___ A ^ B 0x___ A ^ A 0x___

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

0x69 & 0x55 --> 0x______ 0x69 | 0x55 --> 0x______ 0x69 ^ 0x55 --> 0x______

q Used to change or query one or more bits in a variable q The bitmask indicates which bits are to be affected q Common operations:

• Setting one or more bits to 1
• Setting one or more bits to 0
• Reading one or more bits

Bitmasks

q Assume that data is an integer variable (size is unknown) q Set the least significant bit of data to 1 (other bits are unchanged)

Bitmasks – set single bit to 1

data 1 1 1 1 ? mask result wanted 1 1 1 1 1 data = _______________________;

q C statement:

data | 1

q Assume that data is an integer variable (size is unknown) q Set bit 0, 2 and 3 of data to 1 (leave the other bits unchanged):

Bitmasks – set multiple bits to 1

data 1 1 1 ? ? ? mask result wanted 1 1 1 1 1 1 data = _______________________;

q C statement:

data | 0xD

q Assume that data is an integer variable (size is unknown) q Set the least significant byte of data to 0xFF

Bitmasks – set byte to 0xFF

data 1 1 1 1 ? ? ? ? ? ? ? ? mask result wanted 1 1 1 1 1 1 1 1 1 1 1 1 data = _______________________;

q C statement:

data | 0xFF

q Assume that data is an integer variable (size is unknown) q Set the 2nd least significant byte of data to 0xFF

Bitmasks – set another byte to 0xFF

data ? ? ? ? ? ? ? ? 1 1 1 1 mask result wanted 1 1 1 1 1 1 1 1 1 1 1 1 data = _______________________;

q C statement:

data | 0xFF00

q Assume that data is an integer variable (size is unknown) q Set the least significant bit of data to 0:

Bitmasks – clear (set to 0) single bit

data 1 1 1 1 1 ? mask result wanted 1 1 1 1 1 data = _______________________;

q C statement:

data & ~1

q Set one or more bits to 1 q Set one or more bits to 0 q Read one or more bits

Review – Common Bit Operations

Review – What Does This Code Do?

int data = ...; data = data | 0x1;

data ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? | 0x1 1 result ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1

q Answer:

• Set the least significant bit to 1

Review – What Does This Code Do?

int data = ...; data = data | 0x4;

data ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? | 0x4 1 result ? ? ? ? ? ? ? ? ? ? ? ? ? 1 ? ?

q Answer:

• Set bit 2 (third least significant bit) to 1

bit 0 bit 1 bit 2

Review – What Does This Code Do?

int data = ...; data = data | 0xF;

data ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? | 0xF 1 1 1 1 result ? ? ? ? ? ? ? ? ? ? ? ? 1 1 1 1

q Answer:

• Set the four least significant bits to 1

bit 0 bit 1 bit 2 bit 3

Review – What Does This Code Do?

int data = ...; data = data & ~0x1;

data ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? & ~0x1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 result ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

q Answer:

• Clear the least significant bit (set it to 0)

bit 0

q Assume that data is an integer variable (size is unknown) q Clear (set to 0) bits 0, 2 and 4 of data (other bits are unchanged):

Bitmasks – clear (set to 0) multiple bits

data 1 1 ? ? 1 ? mask result wanted 1 1 1 data = _______________________;

q C statement:

data & ~0x15

q Assume that data is an integer variable (size is unknown) q Clear (set to 0) the least significant byte of data

Bitmasks – clear (set to 0) single byte

data 1 1 1 1 ? ? ? ? ? ? ? ? mask result wanted 1 1 1 1 data = _______________________;

q C statement:

data & ~0xFF

Feedback Results

q Review Topics (Today) q Ungraded Practice Quizzes (1/week) q Review Homework q More Hands-on/Labs/C Programming (Coming Up) q Teaching

• Slow Down
• Explain Jargon
• Step-by-step Examples

q When post slides?

q Assume that data is an integer variable (size is unknown) q Clear (set to 0) bytes 0 and 1 of data

Bitmasks – clear (set to 0) multiple bytes

data ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? mask result wanted data = _______________________;

q C statement:

data & ~0xFFFF

q Assume that data is an integer variable (size is unknown) q Determine the least significant bit of data:

Bitmasks – read bit

data 1 1 1 1 ? mask result wanted ? result = _______________________;

q C statement:

data & 1

q Assume that data is an integer variable (size is unknown) q Determine the 2nd least significant bit of data:

Bitmasks – read another bit

data 1 1 1 1 ? 1 mask result wanted ?

q Need to shift

Bitwise Operator: Left Shift <<

q 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

A 1 1 1 1 0xB4 A << 3 1 1 0x___

Bitwise Operator: Right Shift >>

q 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?

char A; 1 1 1 0x34 A >> 3 1 1 0x___ char A; 1 1 1 1 0xB4 A >> 3 1 1 1 0x___

1 1 1 0 0 0

q Uses sign extension for signed types

Bitwise Operator: Right Shift >>

unsigned char A; 1 1 1 0x34 A >> 3 1 1 0x___ unsigned char A; 1 1 1 1 0xB4 A >> 3 1 1 1 0x___

0 0 0 0 0 0

Note: Java has the unsigned shift operator >>> (not available in C)

q Insert 0 to the left for unsigned types

q Determine the 2nd least significant bit of data (size unknown):

Bitmasks – revisit example

data 1 1 1 1 ? 1 data >> 1 ? mask result wanted ? result = _______________________;

q C statement:

(data >> 1) & 1

q Determine the 4th least significant bit of data (size unknown):

Bitmasks – read another bit

data 1 1 ? 1 1 result ? result = _______________________;

q C statement:

(data >> 4) & 1

q Assume that data is an integer variable (size is unknown) q Determine the 2nd least significant byte of data

Bitmasks – read byte

data ? ? ? ? ? ? ? ? 1 1 1 1 1 result ? ? ? ? ? ? ? ? result = _______________________;

q C statement:

(data >> 8) & 0xFF

char c = 0xB5; void print_binary(char c) { /* add code here */ }

Bitwise Operators

q Write code to print all the bits of a character from left

to right (starting with the most significant bit):

1 0 1 1 0 1 0 1

Relations Between Operations

q 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

q 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

Why Bitwise Operators?

Used in Networking

Used in Encryption/ Decryption

Used in Compression

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

~ & | ^ << >>

Review – Bitwise Operators

Contrast: Logical Operators

Logical Operators

q Always return 0 or 1 q False is 0 in C q True is anything nonzero in C q Examples (char data type)

• !0x41 --> _____
• !0x00 --> _____
• !!0x41 --> _____
• 0x69 && 0x55 --> _____
• 0x69 || 0x55 --> _____

&& (Logical AND), || (Logical OR), ! (Logical NOT)

What is the Output?

int a = 0x43, b = 0x21; printf("a | b = %x\n", a | b); _________ Printf("a || b = %x\n", a || b); _________ printf("a & b = %x\n", a & b); _________ printf("a && b = %x\n", a && b); _________

Mental Exercise

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

What did we learn?

q Bit-level operators (&, |, ~, ^, <<, >>)

• Operate on bits (view arguments as bit vectors)

q Logical operators (&&, ||, !)

• Always return 0 (False) or 1 (True)

Midterm Review Topics

q 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

q Bitwise and Logical Operators: AND, OR, NOT, XOR, L&R SHIFT q Unix Commands: ls, cd, mkdir, cp, mv, rm, chmod, pwd, -r, etc

• Absolute and Relative Paths, permissions, navigating directory structure

q C programming and differences with Java q Computer Systems (hw/sw, analog/digital), Data Sizes, etc q Sources: ZyBook, Tarnoff, Slides, Labs and Homework q Problems: Short Answer, MC, True False, and Problem Solving