Lecture 5 Information Storage: Bits, Bytes and Addressing

Information Storage

• Assignment 0 is due on January 26
• Lab 2 is this week

Lecture Contents

• Bits, Bytes, Words, Paragraphs, and Pages will be covered
• Hexadecimal Representation will be covered
• Addressing and Byte Ordering will be covered
• Representing Strings and Code will be covered
• Bitwise and Logical Operations will be covered

Bits

• The bit is the basic unit of information in modern computing
• A bit can store two different values: 0 (no electric current) and 1 (electric current)
• A computer's memory is a collection of elements that store one bit of information each
• Bits are too small to be useful on their own
• Addressing individual bits in memory is complex
• Bits are accessed in packages (bytes, words, paragraphs, or pages)

Data Sizes

• A byte is the "standard" smallest package of bits
• Today, a byte contains 8 bits.
• Bytes were 6-9 bits long
• Bytes are uniquely addressable
• A word is the unit of information access by a CPU
• Words can be 8, 16, 32, 64, or 128 bits, depending on the CPU
• A word is the amount of information transferred between the CPU and main memory in one go
• A paragraph is typically 16 bytes (128 bits)
• A page is typically 4KB (4096 bytes) or 8KB (8192 bytes)
• Page size depends on hardware and the system
• A page is the amount of information transferred between main memory and secondary storage

Memory

• Memory is a physical byte array, where each element has a unique address
• Addresses range from 0 to n-1, where n is the size of the memory

Programmers

• Most programming languages access information at the byte level, at the same level that is addressable in memory
• Since each byte has a unique address, programs can access and manipulate each byte

Hexadecimal Notation

• Bits, bytes, words, and paragraphs are all powers of 2
• Computations often multiplying and dividing by 2
• Multiplying and dividing by 2 in binary is easy (add or remove a 0)
• Writing and reading in binary is difficult
• Octal (base 8) is an altenative

Octal

• Octal is a base-8 number system
• Decimal 8 is Octal 10
• Multiplying a number by 8 adds a 0 to the end
• Every 3-bit number is represented by a single octal digit
• Early bytes were 6 or 9 bits long, so a byte was represented by two or three octal digits, and octal was used in early computer systems
• Today a byte is 8 bits long
• A byte requires 3 octal digits (8/3 = 2.66) to be represented
• Idea: Have the number of bits per digit divides nicely into 8

Hexadecimal

• Idea: Have # of bits per digit divides nicely into 8
• Hexadecimal Number System has 16 digits: 0-9, A-F
• Each digit in hexadecimal can be presented with only 4 bits
• Base 16 multiplies numbers by 16, and then adds a zero at the end
• Avoids conversion mistakes
• Arithmetic rules apply
• Fewer digits
• Multiplying a number by 16 adds a 0 to the end
• Prefix hex representations with 0x

Addressing

• Addressing describes how data is located in memory
• Addressing is relatively standard
• Each byte has a unique address, in increasing order
• Data in memory will uses one or more bytes
• The address of a piece of data is the address of the first byte

Byte Ordering

• Byte ordering is the order of bytes in a piece of data. String byte order depends on the data
• There are two common byte orders for numerical data types, such as Integers (short, int, long), Floats (float, double), Pointers
• Big Endian: bytes are ordered from most significant to least significant
• Little Endian: bytes are ordered from least significant to most significant

Big Endian vs Little Endian

• Byte ordering depends on the CPU
• No order is intrinsically better than the other

Scenarios

• When reading/writing binary data to files
• When receiving/sending binary data over a network
• When exchanging data between different computer architectures
• When debugging and looking at the raw data in memory

Strings

• Strings are stored as a sequence of bytes in memory
• Languages usually use null-terminated string
• A string may consist of 0 or more bytes, none of which is nul (0).
• The string is terminated by a nul (0) character
• A string of n characters takes n+1 bytes to store
• ASCII: American Standard Code for Information Interchange
• Simple, all characters are one byte in size, originally only 7 of 8 bits are used
• Cannot encode non-English characters
• Cannot encode special symbols beyond the standard ones. ` Unicode can encode characters from most known languages UTF-16 uses 2 bytes per character (for most characters) UTF-8 is a variable-length encoding that is the same as ASCII for the first 128 characters. It will assume that all character is ASCII encoding

Key Points

• The fundamental unit of data is the bit, but data is addressed in packages of bytes, words, paragraphs, etc
• Hexadecimal representation aligns with data sizes in the modern computer systems & should be used instead of decimal
• When exchanging binary data between systems, byte ordering is critical because it is hardware-dependent
• Strings are typically stored a nul-terminated sequence of bytes using ASCII or Unicode encoding
• Bit manipulation involves manipulating data values containing the bits

Lecture covers bits, bytes, words and hexadecimal representation. Addressing and byte ordering along with representing strings and code will be discussed. Topics include the bit as the basic unit of information and data sizes.