This is a draft cheat sheet. It is a work in progress and is not finished yet.
Abbreviations and Notations
LSB: Least Significant Bit (right-most) |
MSB: Most Significant Bit (left-most) |
a,b
(lower case): a single bit |
A,B
(upper case): set of bits, e.g. A={a_i}, i=[0,N-1]
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Bit-wise operators
Bool/Bit analogy (helps to remember effect of operators): 1 is TRUE, 0 is FALSE |
While Bool operators ( &&
, ||
, !
- no equivalence for ~
) apply to simple TRUE/FALSE operands, bit-wise operators apply to all bits of their operands (see Example block) |
&
(AND): both operands have 1s |
|
(OR): either or both operands have 1s |
^
(XOR, aka exclusive OR): either but not both operands have 1s |
~
(NOT, aka complement): 1 becomes 0; 0 becomes 1 |
<<
(left-shift): a << n
shifts all bits in a
to the left by n
positions and pads with 0s to the right. |
>>
(right-shift): a >> n
shifts all bits in a
to the right by n
positions and pads with 0s to the left |
If a
is an int, a << n
and a >> n
are equivalent to multiplying an dividing respectively by 2n
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1-Bit Bit-wise Operators Summary
Examples (using A = 1010; B = 1100)
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~
: ~A = 11110101
(the number of 1′s depends on the type of A
) |
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Usage
Bit accessing: 1 << 5 = 100000 TOREVIEW |
Bit-wise Operators as Operations of Sets of Bits
Using ALL_BIT
= 32/64 1s on a 32/64-bit machines |
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Two's Complement (TsC)
Most common number system to encode pos.a dn neg. numbers in a binary number representation of negative integers. One's complement is the alternative but seeimingly never used. |
In TsC, MSB used for int sign ( -
for 1, +
for 0) |
Meaning 1: Mathematical operation on binary numbers (the additive inverse op.) |
Meaning 2: Binary signed number representation based on above mathematical operation, s.t. neg. numbers are represented byt hte TsC of the abs. value |
N
-bit TsC range: [-2N-1, +(2N-1-1)]
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Conversion from TsC representation |
Conversion to TsC representation |
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