Logic Gates

There are AND, OR, XOR, and their inverted versions. Usually takes 2 inputs. Can be extended for n-inputs.

XOR

Returns true iff when the number of true inputs are odd.

Universal gate

A gate is a universal gate iff a collection of that gates can be arranged to implement AND, OR & NOT gates. Can be used to implement any circuit. Is functionally complete.

NAND and NOR gates are universal.

Logical circuit representation

Logical circuits are a abstraction of transistor circuits. The logical circuits can be built using TTL or CMOS.

TTL

Two or more (bipolar junction) transistors are used. 0V for LOW. 5V for HIGH. Power consumption is high (even when idle). Switching is fast. Slow compared to modern CMOS. Low noise margin compared to CMOS.

CMOS

Uses 2 metal oxide semiconductors. Power consumption is very low. High speed. High noise margin.

Note

It is recommended to design CMOS with NAND gates only. NAND gates have more fanout and less power comsumption.

Power consumption

$$\text{Dynamic power consumption} = CV^2 f$$

Here:

• $C$ - Capacitance of the circuit
• $V$ - Supply voltage
• $f$ - Charging frequency of the capacitor

$$\text{Static power consumption} = V I_{\text{leakage}}$$

Here:

• $V$ - Supply voltage
• $I_{\text{leakage}}$ - Leakage current

$$\text{Energy consumption} = \text{Power} \times \text{Time}$$

Logic circuits

	Combinational Logic	Sequential Logic
Memory	No	Yes
Feedback loop	No	Yes
Output	Depends only on input	Depends on input & memory