Binary Logic

Binary Logic and Variables §

• Binary Logic: two-valued logic, e.g., true/false, yes/no, closed/open
• Binary Logic Variables: These can take on two discrete values 0 and 1
  • 0 implies false, no, open, etc
  • 1 implies true, yes, closed, etc

Binary Logic Functions §

• Binary logic functions are functions or expressions of binary variables or other binary functions. They produce an output which is 0 or 1 depending on input values
• A logic function can be defined using a truth table. The truth table indicates the value of the function for each possible input values. For example

x	y	f
0	0	0
0	1	1
1	0	1
1	1	0

Logic Operators §

• Logic operations are needed to make logic functions adnd to manipulate them
• These are three basic logic operators: AND, OR and NOT
• Symbol of logic operators

Logic operator	Symbols	Example
AND	·, nothing	$(x\cdot y,xy)$
OR	+	$(x+y)$
NOT	', overbar	$(x^{\prime },\overline{x})$

• Operators have precedence in the order: (), NOT, AND, OR
• The parentheses () help clarify precedence

Logic gates, their symbols and truth tables §

• Logic operators AND, OR, and NOT are implemented via logic gates (which are implemented using transistors)

AND §

OR §

NOT §

Representation of logic functions §

• A logic function can be represented in multiple ways
• Using an example function, we show 3 methods
  • Algebraic
  • Truth table
  • Schematic