Lecture 5 Bits, Bytes, Words, Paragraphs and Pages

Bits and Bytes

• The bit is the fundamental unit of information; it can store two values: 0 (no electric current) and 1 (electric current).
• Computer memory is a collection of elements, each storing one bit.
• Bits are typically accessed in packages of bytes, words, paragraphs, or pages because single bits are too small to be useful to access by themselves.
• A byte is considered the smallest standard package of bits.
• Today, a byte contains 8 bits, but in the past, bytes ranged from 6-9 bits.
• Bytes are uniquely addressable in memory.
• A word is the unit of information accessed by a CPU, typically 8, 16, 32, 64, or 128 bits.
• A word is the amount of information that can be transferred between the CPU and main memory in one go.
• A paragraph is usually 16 bytes (128 bits).
• A page is typically 4KB (4096 bytes) or 8KB (8192 bytes) depending on the hardware and system.
• A page is the amount of information transferred between main memory and secondary storage.
• Programming languages can access information at the byte level, which contains a unique address in physical memory.

Hexadecimal Notation

• Bits, bytes, words, and paragraphs are all powers of 2.
• Computations often involve multiplying and dividing by 2.
• Multiplying or dividing by 2 easier in binary (adding/removing a 0).
• Octal (base 8) requires 3 digits to represent a byte, but the most significant octal digit is not fully used.
• Hexadecimal (base 16) provides a solution since the number of bits per digit divides nicely into 8 (4 bits per digit).
• Doing everything in hex avoids conversion mistakes and uses fewer digits.
• To convert decimal to hex, repeatedly divide the decimal value by 16. The remainders form digits in the hex representation. (e.g., 23512 (decimal) == 5BD8 (hex)).
• To convert hex to decimal, multiply each hex digit by increasing powers of 16 and add the results (e.g. 5BD8 (hex) == 23512 (decimal)).
• Use the prefix 0x to indicate a value is in hex.

Addressing and Byte Ordering

• Addressing shows how data is located in memory.
• Each byte has a unique address in increasing order, in a relatively standard manner.
• A piece of data in memory consists of one or more bytes, and its address is the address of the first byte.
• Byte ordering refers to the order of bytes in a piece of data.
• The order of bytes for strings depends on the data itself.
• There are two byte orders for numerical data types, such as integers and floating-point numbers.
• Big Endian orders bytes from most significant to least significant.
• Little Endian orders bytes from least significant to most significant.
• Byte ordering depends on the hardware, or CPU.
• Applications for reading and writing binary data to files and receiving and transferring binary data over networks may depend on byte order. Exchanging data between computer architectures and debugging tasks can rely on byte ordering.

Strings and Encoding

• Strings are stored as sequences of bytes in memory and are often null-terminated (end with a 0).
• A string of n characters takes n+1 bytes to store because of the null terminator.
• Strings are commonly encoded in ASCII (1 byte per character) or Unicode (often 2 bytes per character).
• The American Standard Code for Information Interchange (ASCII) typically uses a single byte for all characters, and cannot encode non-English characters or special characters.
• Unicode is able to encode characters from many languages (UTF-16 uses two bytes per character, UTF-8 for English characters).

Machine Code

• Program instructions are stored as sequences of one or more bytes.
• The CPU moves a pointer in memory as it executes program instructions.

Bitwise and Logical Operations

• Individual bits cannot be addressed directly in programs.
• Bytes or words can be used to find bits.
• In C, a byte is the "char" type, and a word is the "int" type.
• test(unsigned char b, int i) right shifts a char, (byte), b, by i and performs a bitwise AND with 1 to get the value of bit i.
• Bitwise operators work on the bits of values, and logical operators test entire values.

Bitwise Operator Summary:

• ~ Negates all bits (~x).
• & Bitwise AND: x & y.
• | Bitwise OR: x | y.
• ^ Bitwise XOR: x ^ y.
• >> Right shift: x >> 3 (shifts bits 3 places to the right).
• << Left shift: x << 3 (shifts bits 3 places to the left).

Logical Operator Summary:

• ! Negates a value: !x (0 if x is non-zero, 1 if x is zero).
• && Logical AND: x && y (1 if both x and y are non-zero, else 0).
• || Logical OR: Example: x || y (1 if either x or y is non-zero, else 0).

Explanation of bits, bytes, words, paragraphs and pages. The bit is the fundamental unit of information; it can store two values: 0 and 1. Computer memory is a collection of elements, each storing one bit. A byte is the smallest standard package of bits.