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Bit Manipulation. when every bit counts. Questions on Bit Manipulation. what is the motivation for bit manipulation what is the binary, hexadecimal, octal numbers? why are they used?
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Bit Manipulation when every bit counts
Questions on Bit Manipulation • what is the motivation for bit manipulation • what is the binary, hexadecimal, octal numbers? why are they used? • what are the following numbers in decimal 012, 0b111, 0xA1, 23? Convert 11 decimal into binary, octal, hexadecimal. • What is bitwise OR, bitwise AND, bitwise exclusive OR, bitwise complement, left and right shift? how are they denoted and how are they computed? • what is sizeof? • What is called a mask and how is it used? • what are bit fields?
Why Bit Manipulation • extremely efficient and compact way of data storage and processing • a way of low-level interaction with peripheral devices: mice, disks, scanners, etc. • memory and compute cycles are cheap, bit manipulating programs are cryptic. Do not use unless you have to
Bits • Bit - elementary unit of information storage • can store either 1 or 0 • Electronic circuits are most robust and dependable if they have at most two stable states • computer data is stored and processed as sequences of bits • more complex data types are encoded in bit sequences • How are signed/unsigned integers are represented? Floating point data? Characters? • base for numeric representation can be binary, decimal, octal or hexadecimal • octal constant has leading 0: 012 == 10 • hexadecimal has leading 0x: 0x12 == 18 • binary has leading 0b: 0b11 == 3 • octal and hexadecimal simplify conversion to binary base • octal digit represents three binary digits 012 means 001 010 (binary) • hexadecimal – four binary digits 0x12 means 0001 0010 (binary)
Conversion with Decimal Base • to decimal 0651 = 6*8^2 + 5*8^1 + 1*8^0 = 425 0x1B6 = 1*16^2 + 11*16^1 + 6*16^0 = 438 0b10101 = 1*2^4 + 1*2^2 + 1*2^0 = 21 • from decimal 425 %8 438 %16 21 %2 53 1 27 6 10 1 6 5 1 11 5 0 ------ -------- 2 1 0651 0x1B6 1 0 ------- 0b10101
Input/Output in Bases • a number may be input or printed in decimal (default) octal or hexadecimal using stream manipulators dec - decimal oct - octal hex – hexadecimal • to use – input/output manipulator to stream cin >> oct >> myNumber; // inputs in octal cout << hex << myNumber; // outputs in hexadecimal • remember the same number can be input/output using any of the bases
Bitwise Operations • treat data as a sequence of bits rather than complex data type • unsigned (int) – good data type to use • operations • & - bitwise and: 1 only if both operands are 1 101111 &011010 001010 • | - bitwise or: 1 if at least one operand is 1 • ^ - bitwise exclusive or: 1 only if exactly one operand is 1 • ~ - bitwise complement: single operand, 1s to 0, 0 to 1 • << - left shift: shifts bits to left (by specified number of positions), right bits are filled with 0-oes: if variable a is 0010 then (a << 2) is 1000 • this operation looks familiar, what is it? • >> - right shift: shifts bits to right, left bits are filled with 0-oes • compound assignment is allowed for all operations: a &=0x001; • useful function: sizeof(type or class)
Bit Fields • can specify fewer bits in integer member variables of structures and classes • example class card { private: unsigned face : 4; // 4 bits; 0-15 unsigned suit : 2; // 2 bits; 0-3 unsigned color : 1; // 1 bit; 0-1 };
