Fundamental Hardware Elements of Computers: Gate conversion

Sometimes it is cheaper to create circuits using only one sort of gate, and you might be asked to do so in the exam. These gates tend to be NAND & NOR gates. "But how can you create complex circuits by using only one type of gate?!" you may well ask. We'll now cover how other gates can be made from NAND & NOR gates:

Step	NOR Gate	Equivalent
Diagram
Description	If you split the same input (A) and feed it into NOR both gate inputs you create a NOT Gate
Truth Table	Because: A A $A+A$ ${\overline {A+A}}$ ${\overline {A}}$ 0 0 0 1 1 1 1 1 0 0

Step	NAND Gate	Equivalent
Diagram
Description	If you split the same input (A) and feed it into both NAND gate inputs you create a NOT Gate
Truth Table	Because: A A $A.A$ ${\overline {A.A}}$ ${\overline {A}}$ 0 0 0 1 1 1 1 1 0 0

Exercise: Gate Conversion Render the following boolean equations using only NAND gates: ${\overline {{\overline {A}}.B}}$ Answer: ${\overline {A}}.{\overline {B}}$ Answer: Now try the similar questions using only NOR gates (you might need De Morgan's Law to help you out here, or use a truth table to simplify things) $A+{\overline {B}}$ Answer: ${\overline {A}}.{\overline {B}}$ Answer: Why might you want to use only one sort of gate to create a circuit? Answer: It might be cheaper to make circuits with only one sort of gate, it might make for simpler circuits