Lecture 001

Lab 0 no grace submission, released. Due Friday 11:59pm

Bits

Bits: 0s or 1s, but represented between 0.0V and 1.1V (vultage). There exists transition period.

• we can count fingers in binary instead of unary

• represent int

• represent scientific notation [?]

• represent double [?]

Byte: 8 bits (256 different values, represent in Hexadecimal, base 16) Hexadecimal: one hex is 4 bits

Datatype in C

• Linux: long and pointer stay in the same size

• Windows: long stay the same size depend on your x86 or x86-64

• (in this course, assume x86-64 and the image above)

Operators

Boolean Algebra: developed by George Bool

• And

• Or

• Not

• Xor: or but, not both, or two value not the same

Bit Vector:

• using Boolean Algebra on Bit Vectors (bit-wise operation)

  

Representing, Manipulating Sets using bits

Logical Operators

Operators: &&, ||, !

• has early termination

• any anything non-zero is True

• result only True or False, represented by 0x01 and 0x00

• NULL is a pointer, equivalent to 0x00 or False

Shifts: (good for hardware)

• << left shift: filling with 0s

• >> right shift

  • logical shift (for unsigned): filling with 0s
  • arithmetic shift (for signed): replicate with left most

• undefined behavior: shift < 0 or >= word size. But shifting by 3 followed by shifting by 1 does not behave the same as shifting by 4. Example: if shifting by 4 will result undefined, and shifting by 3 will not, then shifting by 3 and 1 is allowed.

Twos Complement

Negation with twos complement: easy

Unsigned representation: [0, 2^w - 1] Twos complement: [-2^(w-1), 2^(w-1) - 1]

Observation:

• negate int_min = int_min

• uint_max = 2 * int_max + 1

• positive number in signed and unsigned are the same

Preserving Bit Pattern

constants are int32 in C unsigned constants has a U as suffix.

Casting:

• casting with parenthesis

• implicit casting with function input

• implicit casting because being in the same expression

If there is a mixed signed and unsigned in expression, everything will be cast to unsigned (therefore using unsigned relation).

• the image above shows the true relation when the computer interpret it and the evaluation based on signed relation or unsigned relation

Extension and Trunking

Extension: extend left bits (keep negative) to preserve value

Trunking: just cut down if you can actually represent (not losing representation). Otherwise, keep bit pattern

• small positive: okay

• large positive: actual value minus the highest weight

• small negative: okay

• very negative: positive cuz the left most after operation is likely 0

TODO: what is x86 and x86-64 represent TODO: review 15122 bits