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# Digital Electronics

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Tweet## Odesma Dalrymple

on 14 March 2012#### Transcript of Digital Electronics

Digital Electronics Function: to generate digital output from digital input The operation of digital electronics falls under two classes Sequential Logic Combinational Logic Outputs are only dependent on the present input states

All functions can be performed using LOGIC GATES gates are devices that perform operations of Boolean algebra applied to two-state (binary) systems Examples Functions:

Taking two 16-bit numbers as inputs and generating a 16-bit (plus carry) sum (Adder - http://www.electronics-tutorials.ws/combination/comb_7.html)

Comparing two number to see which is larger

Taking numbers expressed in binary and displaying them as decimal characters Outputs are dependent on current and past inputs

Digital memory of some sort is needed Examples Functions:

Converting a string of bits in serial form into a parallel set of bits

Keeping count of the number of 1's in a sequence

Giving 1 output pulse for each 4 input pulses Logic Gates OR Gate Output is HIGH if one of more inputs is HIGH Gates can have any number of inputs, but standard packages usually contain:

four 2-input gates

three 3-input gates

two 4-input gates four 2-input gates The Boolean symbol for OR is + Truth Table for 2-inputs A B A+B A.B AND Gate Output is HIGH only of all inputs are HIGH four 2-input gates The Boolean symbol for AND is . Truth Table for 2-inputs A B A' Inverter (The NOT function) Output is the complement of the INPUT six 1-input gates The Boolean symbol for NOT is ' Truth Table A NAND and NOR INVERTER Combined with AND or OR gates Truth Table for 2-inputs A Exclusive-OR and Exclusive-NOR (A.B)' B NAND B A (A+B)' NOR four 2-input gates four 2-input gates A (A.B)' B XOR B A (A+B)' XNOR four 2-input gates four 2-input gates Output is HIGH if only one of two inputs is HIGH Output is HIGH if both inputs are either HIGH or LOW Truth Table for 2-inputs Making Gates from Discrete Components If either input is LOW the output is LOW

The output goes HIGH only when both inputs are HIGH If either or both inputs are HIGH the output is HIGH

The output goes LOW only when both inputs are HIGH

resistor-transistor logic was popular in 1960's due to low cost, but is now obsolete A HIGH at either or both outputs turns on at least one transistor, pulling the output LOW Disadvantages of Logic Constructed from discrete components Can't use many of them in a row

Any load at the output is seen by the signal at the input

It is a slow responding circuit due to resistive pull-up Gate Circuit Task: To sound a buzzer if either car door is open and the driver is seated Assumptions

Input is HIGH if door is open

Input is HIGH if driver is seated Q = (L+R).S where L and R refer to the HIGH input at the left and right door respectively and S refers to the HIGH input at the driver's seat Assumptions

Input is LOW if door is open

Input is LOW if driver is seated If the Assumptions are different circuit is opened Q = ((L'.R')+S')' where L' and R' refer to the LOW input at the left and right door respectively and S' refers to the LOW input at the driver's seat Gate Interchangeability It is possible to form one kind of gate from another =

Full transcriptAll functions can be performed using LOGIC GATES gates are devices that perform operations of Boolean algebra applied to two-state (binary) systems Examples Functions:

Taking two 16-bit numbers as inputs and generating a 16-bit (plus carry) sum (Adder - http://www.electronics-tutorials.ws/combination/comb_7.html)

Comparing two number to see which is larger

Taking numbers expressed in binary and displaying them as decimal characters Outputs are dependent on current and past inputs

Digital memory of some sort is needed Examples Functions:

Converting a string of bits in serial form into a parallel set of bits

Keeping count of the number of 1's in a sequence

Giving 1 output pulse for each 4 input pulses Logic Gates OR Gate Output is HIGH if one of more inputs is HIGH Gates can have any number of inputs, but standard packages usually contain:

four 2-input gates

three 3-input gates

two 4-input gates four 2-input gates The Boolean symbol for OR is + Truth Table for 2-inputs A B A+B A.B AND Gate Output is HIGH only of all inputs are HIGH four 2-input gates The Boolean symbol for AND is . Truth Table for 2-inputs A B A' Inverter (The NOT function) Output is the complement of the INPUT six 1-input gates The Boolean symbol for NOT is ' Truth Table A NAND and NOR INVERTER Combined with AND or OR gates Truth Table for 2-inputs A Exclusive-OR and Exclusive-NOR (A.B)' B NAND B A (A+B)' NOR four 2-input gates four 2-input gates A (A.B)' B XOR B A (A+B)' XNOR four 2-input gates four 2-input gates Output is HIGH if only one of two inputs is HIGH Output is HIGH if both inputs are either HIGH or LOW Truth Table for 2-inputs Making Gates from Discrete Components If either input is LOW the output is LOW

The output goes HIGH only when both inputs are HIGH If either or both inputs are HIGH the output is HIGH

The output goes LOW only when both inputs are HIGH

resistor-transistor logic was popular in 1960's due to low cost, but is now obsolete A HIGH at either or both outputs turns on at least one transistor, pulling the output LOW Disadvantages of Logic Constructed from discrete components Can't use many of them in a row

Any load at the output is seen by the signal at the input

It is a slow responding circuit due to resistive pull-up Gate Circuit Task: To sound a buzzer if either car door is open and the driver is seated Assumptions

Input is HIGH if door is open

Input is HIGH if driver is seated Q = (L+R).S where L and R refer to the HIGH input at the left and right door respectively and S refers to the HIGH input at the driver's seat Assumptions

Input is LOW if door is open

Input is LOW if driver is seated If the Assumptions are different circuit is opened Q = ((L'.R')+S')' where L' and R' refer to the LOW input at the left and right door respectively and S' refers to the LOW input at the driver's seat Gate Interchangeability It is possible to form one kind of gate from another =