Digital Logic 1/Digital Signals and Logic Symbols

Basic Ideas and Concepts

• Learn what is referred to as a "digital" circuit
• Learn the respective logic gates and symbols associated
• Learn the functionality of each logic gate

Digitization

When we say we have a "digital" circuit, it means that we create an entire new domain that is purely represented by an analog signal. What that means is, referring back to our basic circuit of a voltage source and a resistor, we can say that the different voltage levels can represent a "low" or "high". Using electrical and computer engineering conventions, we classify a logic "high" as anywhere from 4.5 volts to 5.0 volts and a logic "low" as anywhere from 0.1 to 0.5 volts.

So basically, we say that a 0 is inputted when the voltage is between 0.1-0.5 volts and a 1 if the voltage is 4.5-5 volts. Ideally however, we want 0.0 and 5.0 volts to represent 0 and 1 respectively and pictorially is represented below.

high 1 or on	low 0 or off
X 100M X 100K X 100 X 100m X 100μ Ω A DC AC C L	X 100M X 100K X 100 X 100m X 100μ Ω A DC AC C L

With this in mind, we can now move on and discuss logic gates which form the foundation of combinational circuits and analysis.

Logic Gates

Below are all the different logic symbols that are used to design and implement digital circuits.

Type	Distinctive shape	Rectangular shape	Mathematical Representation	Truth table
AND Gate			$A\cdot B$	INPUT OUTPUT A B A AND B 0 0 0 0 1 0 1 0 0 1 1 1
OR Gate			$A+B\!$	INPUT OUTPUT A B A OR B 0 0 0 0 1 1 1 0 1 1 1 1
NOT Gate			${\overline {A}}$	INPUT OUTPUT A NOT A 0 1 1 0
Note about NOT gate In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a logical inversion between the external logic state and the internal logic state (1 to 0 or vice versa). On a circuit diagram it must be accompanied by a statement asserting that the positive logic convention or negative logic convention is being used (high voltage level = 1 or high voltage level = 0), respectively). The wedge is used in circuit diagrams to directly indicate an active-low (high voltage level = 0) input or output without requiring a uniform convention throughout the circuit diagram. This is called Direct Polarity Indication. See IEEE Std 91/91A and IEC 60617-12. Both the bubble and the wedge can be used on distinctive-shape and rectangular-shape symbols on circuit diagrams, depending on the logic convention used. On pure logic diagrams, only the bubble is meaningful.
NAND Gate			${\overline {A\cdot B}}$	INPUT OUTPUT A B A NAND B 0 0 1 0 1 1 1 0 1 1 1 0
NOR Gate			${\overline {A+B}}$	INPUT OUTPUT A B A NOR B 0 0 1 0 1 0 1 0 0 1 1 0
XOR Gate			$A\oplus B$	INPUT OUTPUT A B A XOR B 0 0 0 0 1 1 1 0 1 1 1 0
XNOR Gate			${\overline {A\oplus B}}$ or ${A\odot B}$	INPUT OUTPUT A B A XNOR B 0 0 1 0 1 0 1 0 0 1 1 1