Data Representation

There are may ways to represent numbers. Consider...

• Roman Numerals

• Arabic Numerals

• Base 2

• Base 8, or Octal Numbers, are represented by grouping three binary digits.

  • Used in chmod 600 foo.txt

• Hexadecimal groups 4 binary digits for base 16. Uses numbers 0-9 and letters a-f.

Bytes

On modern computers, data is accessed in chunks of 8 bits, which is the same as 1 byte.

• E.g., a char data type in C is 1 byte.

Larger chunks of data (called "words") are formed from multiple bytes (which are all powers of two because it doubles the number of bits):

• 2 bytes = 16 bits
• 4 bytes = 32 bits
• 8 bytes = 64 bits

Modern CPUs have instructions for doing operations on each word-sized data values.

C Data Types

C is supposed to be one step above assembly language.

The "primitive" C data types typically map onto machine word sizes (not consistent across different machines and compiler, though).

"Typical" representations of C data types include (data type | bytes used on 32-bit systems | bytes used on 64-bit systems):

• char | 1 | 1
• short | 2 | 2
• int | 4 | 4
• long | 4 | 8

Note the difference on the last line! The reason long is different is because long is represented using pointers, and on 64-bit systems, pointers are larger.

Portable Integer Types stdint.h header files provide protable integer types providing an exact number of bits: int32_t, uint32_t, int64_t, uint64_t, etc

If you write code for different systems, be careful when using constants.

• For example, 0x100000000UL (232) is likely to be a valid on a 64-bit system but not on a 32-bit system
• Note: the “UL” suffix means “unsigned long”