Chapter 2 Flashcards
logic circuits are made up of ____
logic gates - fundamental building blocks that carry out the logic operations
fundamental elements of a digital system are _____ and _____
input variable and output function
AND logic
if both (or all) inputs are 1, then output is 1
otherwise output is 0
represented by multiplication
two gates in series
OR logic
if any inputs are 1, then output is 1
if all inputs are 0, then output is 0
represented by addition
two gates in parallel
NOT logic
switches the input’s value from 0 to 1 or 1 to 0
aka the complement of a variable
NAND gate
output is complement of the AND of the inputs
NOR gate
output is the complement of the OR of the inputs
XOR gate
output is 1 if an odd number of input variables is 1
represented with a circle around an addition symbol
what is the xor function equivalent to
AB’ + A’B
truth table
used to demonstrate the output for each possible combination of inputs of a combinational circuit
universal logic gate
gates that can be used to implement the function of and, or, and not
NOT from NAND gates
both inputs of NAND gate are the same (split input into to wires, then feed into NAND)
AND from NAND gates
- first have A and B go into 1 NAND Gate, then feed output from 1st NAND gate (AB)’ into both inputs of 2nd NAND gate((AB’)’) = AB
OR from NAND gates
- first not both inputs
- then feed the not outputs into a third nand gate
NOT from NOR gates
- same as NAND
- connect inputs together
OR from NOR
- same as AND from NAND
- put inputs into one NOR gate then NOT the output from the first NOR gate
AND from NOR
- same as OR from NAND
- not each input, then feed them into the same NOR gate
NAND from NOR
- use same procedure to get AND from NOR, then NOT it
NOR from NAND
- use same procedure to get NOR from NAND then NOT it
logic network analysis - timing diagrams
tracks the sequential series of 0 and 1 for input and the output for those inputs
propogation delay
- t(pd)
- time for a change in the input of a gate to propagate to the output
- there are high to low and low to high propagation delays
what does the complement of a function look like?
- apply demorgans theorem until all ands have become ors and all ors have become ands
- the nots should change
why is simplifying logic circuits important?
- less cost
- less size
- less power consumption
- less delay
- speed is higher
minterms
- products of all variables
- labelled as a product of the variables, when variable is 0, it is x’, when the variable is 1, it is x
SOP
- sum of products
- sum of all minterms that result in the output being 1
- fully defines the design of the function
Standard SOP
- has all variables represented in each term
- not the simplified version
- can be obtained from a simplified version by multiplying each term with the missing variable in the form (A + A’)
maxterms
- sum of the variables for each result
- if variable’s value is 0, it is represented by x
- if value is 1, its represented by x’
eg. x + y + z
POS
- product of sum
- product of all maxterms that result in output being 0
Integrated circuits
- IC is fabricated on a die of a silicon semiconductor crystal (AKA a chip) containing the electronic components for constructing digital gates
- the gates are interconnected to form the required circuit
- chip mounted on a container and connections are welded to external pins (number of pins varies)
small scale integration
- number of gates fewer than 10
- limited by the number of pins available in the IC
medium scale integration
-number of gates 10 - 1000
- usually perform specific elementary digital operations (decoders, adder, multiplexer, register, counter)
large scale integration
- thousands of gates
- digital systems such as processors, memory chips, programmable logic devices
very large scale integration (VLSI) and ultra large scale integration (ULSI))
- millions of gates
- large memory arrays and complex microcomputer chips
digital logic families
TTL - transistor transistor logic
ECL - emitter-coupled logic
MOS - metal oxide semi-conductor
CMOS - complementary metal oxide semiconductor
Fan-out
- number of inputs that can be connected to a single output
Fan-in
number of inputs available in a gate (aka number of inputs that can be connected to a circuit)
Power dissipation
power that must be available from the power supply for a gate to consume
propogation delay is inversely proportional to ______________
operating speed
noise margin
max external noise voltage added to an input signal that doesn’t cause an undesirable change in the output
mos
- metal oxide semiconductor
- a transistor with 3 terminals:
1. source - input terminal
2. drain - output terminal
3. gate - terminal where an electrical signal is applied to control current flow from source to drain
