Boolean Algebra

Distributive property

$$\begin{array}{rl}a\&(b\mid c)& =(a\&b)\mid (a\&c)\\ a\mid (b\&c)& =(a\mid b)\&(a\mid c)\end{array}$$

Playing with the XOR (^) operator

• We have a ^ a = 0, where 0 represents a vector (bits) of all zeroes
• This property holds even when the terms of an expression are re-arranged, leading to interesting expressions like:

$$(a{}^{\wedge }b){}^{\wedge }a=b$$

Shift operations

• Left shift
• Right shift
  • Two types of right shift:
    • Logical right shift
    • Arithmetic right shift

Sources

• Computer Systems - A Programmer’s Perspective

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