logic circuits
Succeeds: propositions
Summary
Logic gates
| Operation | Gate | Output |
|---|---|---|
| NOT |  | |
| AND |  | |
| OR |  | |
| NAND |  | |
| NOR |  | |
| XOR |  | |
| XNOR |  |
hollow circle represents a negation, solid circle represents a wire intersection
Universal gates
| Operation | NAND | NOR | ||
|---|---|---|---|---|
| NOT |  |  | ||
| AND |  |  | ||
| OR |  |  |
Half adder
- arithmetic addition of 2 single bits
- 2-bit output
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
Full adder
2-bit comparator
Concept
Logic circuits
- circuit made up of logic gates
- combinational circuits: output depends entirely on inputs
- sequential circuits: output depends on inputs and state
- fan in -> number of inputs to a gate
- every input must be connected for the circuit to work
Universal gates
- any boolean function can be built using only NOT, AND and OR
{NOT, AND, OR}is a complete set of logic
NAND circuits
- NAND can implement NOT, AND and OR
{NAND}is a complete set of logic- for SOP expressions
NOR circuits
- NOR can implement NOT, AND and OR
{NOR}is a complete set of logic- for POS expressions
Application
SOP to NAND circuit
POS to NOR circuit
