Basic Digital Logic Basic Gates

Digital Signals Digital Signals have two basic states: 1 (logic “high”, or H, or “on”) 0 (logic “low”, or L, or “off”) Digital values are in a binary format. Binary means 2 states. A good example of binary is a light (only on or off)

Digital Logic Hardware consists of a few simple building blocks These are called logic gates AND, OR, NOT, … NAND, NOR, XOR, … Logic gates are built using transistors NOT gate can be implemented by a single transistor AND gate requires 3 transistors Transistors are the fundamental devices Pentium consists of 3 million transistors Compaq Alpha consists of 9 million transistors Now we can build chips with more than 100 million transistors Functionality can be expressed by a truth table A truth table lists output for each possible input combination

Basic Gates Basic Digital logic is based on 3 primary functions (the basic gates): NOT Gate AND Gate OR Gate Other gates XOR Gate NAND Gate NOR Gate XNOR Gate

The AND function Usually represented by dot (.) Ex: x.y Logics: If all the inputs are high is the output is high If any input is low, the output is low

AND Logic Symbol Output Inputs If both inputs are 1, the output is 1 If any input is 0, the output is 0

AND Logic Symbol Inputs Output Determine the output

AND Logic Symbol Inputs Output 1 Determine the output

AND Logic Symbol 1 1 Inputs Output 1 Determine the output

AND Truth Table To help understand the function of a digital device, a Truth Table is used: Input Output 1 Every possible input combination Truth Table for 3 inputs AND Gate

AND Gates It is possible to have AND gates with more than 2 inputs. The same logic rules apply – “if any input…”

AND Different Symbols X & Y X and Y X Y X * Y XY (textbook) and(Z,X,Y) V U

The OR Gate Usually represented by dot (+) Ex: x+y The OR function: if any input is high, the output is high if all inputs are low, the output is low

OR Logic Symbol Output Inputs If any input is 1, the output is 1 If all inputs are 0, the output is 0

OR Logic Symbol Inputs Output Determine the output

OR Logic Symbol 1 Inputs Output 1 Determine the output

OR Logic Symbol 1 1 Inputs Output 1 Determine the output

OR Truth Table Truth Table Input Output 1 Truth Table for 3 inputs 1 Truth Table for 3 inputs OR Gate

NOT Y = ~X Y = !X Y = not X Y = X’ Y = X Y = X (textook) not(Y,X)

The NOT function The NOT function: If any input is high, the output is low If any input is low, the output is high “The output is the opposite state of the input” The NOT function is often called INVERTER

NOT Logic Symbol Input Output If the input is 1, the output is 0

NOT Logic Symbol Output Input 1 Determine the output

NOT Logic Symbol 1 Output Input Determine the output

NOT Truth Table Truth Table Input Output 1 NOT Function

Exercise 1 1. Least Challenging Complete the sentences: If all inputs of an OR gate are low, the output is_________ If any input of an AND gate is low, the output is _________ The output of a NOT gate is always the ___________ of the input.

Chips

The XOR [Exclusive OR] function Usually represented by  Ex: x  y Logics: If all inputs are high or low then the output will be low Y X + = Å

XOR Logic Symbol X Z Output Inputs Y B A + = Å

XOR Logic Symbol Inputs Output Determine the output

XOR Logic Symbol 1 Inputs Output 1 Determine the output

XOR Logic Symbol 1 1 Inputs Output Determine the output

XOR Logic Symbol 1 Inputs Output 1 Determine the output

XOR Truth Table Truth Table for 3 inputs XOR Gate

The XNOR [Exclusive NOR] function Usually represented by Ex: X Y or (x  y)′ Logics: If all inputs are high or low then the output will be high

XNOR Logic Symbol X Z Output Inputs Y X Y =XY+X′Y′

XNOR Logic Symbol 1 Inputs Output Determine the output

XNOR Logic Symbol Inputs Output 1 Determine the output

XNOR Logic Symbol 1 Inputs Output Determine the output

XNOR Logic Symbol 1 1 Inputs Output 1 Determine the output

XNOR Truth Table Truth Table for 3 inputs XNOR Gate

The NAND [NOT-AND] function Usually represented by ′ or ‾ Ex: (XY)′ Logics: If all inputs are high output will be low

NAND Logic Symbol Output Inputs

NAND Logic Symbol 1 Inputs Output Determine the output

NAND Logic Symbol 1 Inputs Output 1 Determine the output

NAND Logic Symbol 1 1 Inputs Output Determine the output

NAND Logic Symbol 1 Inputs Output 1 Determine the output

NAND Truth Table Truth Table for 3 inputs NAND Gate

The NOR [NOT-OR] function Usually represented by ′ or ‾ Ex: (X+Y)′ Logics: If all inputs are low output will be high

NOR Logic Symbol Inputs Output

NOR Logic Symbol 1 Inputs Output Determine the output

NOR Logic Symbol Inputs Output 1 Determine the output

NOR Logic Symbol 1 Inputs Output Determine the output

NOR Logic Symbol 1 Inputs Output 1 Determine the output

NOR Truth Table NOR Gate Truth Table for 3 inputs

Draw a circuit diagram for  = (xy' + x'y)z.

(A.B+C′)D