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three most important encoding of numbers:

unsigned integers
signed integers
float-point number

we need to focus on:

the ranges of values that can be represented
- overflow
- roundoff
the properties of different arithmetic operations
- integer arithmetic satisfy commutative and associative
- float-point arithmetic is commutative, but not associative

Information Storage

virtual memory -> larger bytes array -> bytes -> block of eight bits
virtual address space -> each memory bytes has a unique number

in C, pointer’s value is the virtual address of the object’s first bytes
compiler use the pointer’s type to generate machine code to access object’s value

Hexadecimal Notation

binary, decimal and hexadecimal

write bit pattern as base-16 or hexadecimal number

word size of a computer indicates the noraml size of integer and pointer data
virtual address is encoded by a word, the word size is the maximum size of the virtual address space
n word size -> [0, 2^n] virtual address space

Data Sizes

different data type may have different size depend on the machine and compiler

Addressing and Byte Ordering

object that span multiple bytes, we must establish two conventions:

what will be the address of the object: smallest address of the bytes used
how will we order the bytes in memory: big endian and little endian

when byte ordering becomes a issue:

binary data is communicated over a network between different machines
programs are written that circumvent the normal types system

Representing String

in C, string is an array of characters terminated by the null character

Representing Code

different machine use different and incompatible instructions and encodings
binary code is seldom portable across different combinations of machine and operating sytem