CSAPP笔记：Bits, Bytes and Integer01

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CSAPP笔记：Bits, Bytes

Representing information as bits

Everything is bits

• 0/1
• encoding/interpreting sets of bits in various ways
  • instructions
  • represent and manipulate numbers. sets and strings
• why use bits?
  • easy to store
  • reliably transmitted on noisy and inaccurate wires

Encoding Byte Values

• Binary 00000000-11111111
• Decimal 0-255
• Hexadecimal 00-FF

Example Data Representations

Bit level manipulation

Boolean algebra

Example: Representing and manipulating Sets

widely used

• symmetric difference is 对称差 in chinese:

shift

• left shift
• right shift
  • logical shift
  • arithmetic shift
• undefined behavior
  • shift amount < 0 or >= word size

Integers

Representing signed and unsigned

Encoding Ints

Unsigned

Signed

• for two’s complement, most significant bit indicated sign
  • 0 for nonnegative
  • 1 for negative

Numeric Ranges

Unsigned

0 ~

Two’s Complement(universal)

~

Minus 1

1111…111

values for W = 16

values for different word sizes

• 64bits TMax has 18 位

Conversion, Casting

Mapping between Signed & Unsigned

• keep bit representations and reinterpret

• casting may cause some surprises , we need to be careful
  • 0 == 0U
  • -1 < 0
  • -1 > 0U
  • 2147483647U < -2147483648

what does this code return for TMin?

• it will return TMin(100…000)

why UMax = 2TMax+1?

What if i is declared unsigned?

• infinite loop: 0->UMax

another example

• infinite loop

Expanding, Truncating

Sign Extension

example:

• the above is a negative number

Truncating

• it’ so funny here, the professor does the additions wrongly for two times

• it wasn’t a very interesting example :)

• positive number may become negative number
• negative number may become positive number