Logic Gates Flashcards
What is a gate?
A device that performs a basic operation on electrical signals
Consist of transistors
What are circuits?
Gates combined to perform more complicated tasks
What are boolean expressions?
Uses Boolean algebra, a mathematical notation for expressing two-valued logic
What are logic diagrams?
A graphical representation of a circuit; each gate has its own symbol
What are truth tables?
A table showing all possible input values and the associated output values
What is functional notation?
Uses a function name followed
by a list of arguments in place of
the operands used in Boolean
expressions
What are the two main roles of transistors?
amplifier or binary switch
What is a NOT gate? What are notations?
accepts one input signal (0 or 1) and returns the opposite signal as output, sometimes referred to as an inverter
X= A′= Ā= ¬A
Why do we need to use transistors?
need to be able to implement the logic
functions in hardware and need to be able to pass the output
of one function to an input of another
they are power efficient and fast
What is an AND gate? Notation?
accepts two signals (0 or 1)
returns a 1 if both signals are one, if not it returns a 0
X=A*B
What is an OR gate? Notation?
accepts two signal (0 or 1)
returns a 0 if both inputs are zero otherwise it outputs a 1
X= A + B
What is the NAND gate? Notation?
(NOT of AND gate)
accepts two input signals, if both are 1 the output is 0 otherwise the output is 1
X=(A*B)’
What is the NOR gate? Notation?
(NOT of OR gate)
accepts two inputs, If both are 0, the output is 1; otherwise, the output is 0
X = (A+B)’
Can some gates be generalized to accept three or more input values?
yes
What would a three input AND gate act like?
will produce an output of 1 only if all input values are 1
What is the XOR gate? Notation?
accepts only two input signals, if both inputs are the same the output is 0, otherwise it is 1
X= A (circle with cross) B
What is the boolean and functional notation of NOT gate?
X=A’
X=NOT(A)
What is the boolean and functional notation of OR gate?
X = A + B
X=OR(A,B)
What is the boolean and functional notation of AND gate?
X = A * B
X=AND(A,B)
What is the boolean and functional notation of NOR gate?
X = (A + B)’
X=NOT(OR(A,B))
What is the boolean and functional notation of NAND gate?
X = (A * B)’
X=(NOT(AND(A,B))
How can you define the XOR function in functional and boolean notation in terms of AND, OR, and NOT? How can the XOR function be simplified?
X = (A + B) * (A * B)’
X = AND(OR(A,B),NOT(AND(A,B)))
X = NOT(A=B)
X = A<>B
How are circuits combined?
by using the output of one gate as the input for another
How many rows in a truth table are required to show all outcomes for three inputs?
8
What is the distributive law of boolean algebra?
you can turn X=AB + AC (3 gate circuit) into X=A * ( B + C) (2 gate circuit)
How are addition operations carried out at the digital logic level?
special circuits called adders
What is the difference between a half adder and a full adder?
half: computes the sum of two bits and produces the correct carry bit
full: computes the sum of two bits and a carry bit and produces the correct carry bit
How many cases is evaluated to 1 in AND gate?
1 (input of 1,1)
How many causes evaluate to 1 in XOR gate?
2 (1,0 and 0,1)
What is a general formula to find the number of rows in a truth table given the number of inputs?
2^n
n is number of rows
