chapter 4 gates Flashcards
what are gates ?
what are circuits?
what are transistors
gates: A device that performs a basic operation on electrical
signals
circuits: Gates combined to perform more complicated tasks
transistors: Very small electronic switches that acts like a switch ( open (0) and closed (1))
how do you describe the behavior of gates and circuits?
3 parts
1.boolean expressions
2.logic diagrams
3.truth tables
what are the six types of gates?
NOT
AND
OR
XOR
NAND
NOR
NOT Inverts its single input
AND Produces 1 if all input values are 1
OR Produces 0 if all input values are 0
XOR Produces 0 if both input values are the same
NAND Produces 0 if all input values are 1
NOR Produces 1 if all input values are 0
what does a NOT gate look like?
what is the expression?
what is the truth table?
how many inputs accepted?
Look like : a triangle with a circle on the end
expression: x = A’
truth table
0 1=1
1 1 =0
input: one and returns the complementary (opposite) signal as output
what does a AND gate look like?
what is the expression?
what is the truth table?
how many inputs accepted?
Look like : a square with a round edge on it
X = AB or X = A . B
everything is zero but 1 + 1 =1
input two signals
what does a OR gate look like?
what is the expression?
what is the truth table?
how many inputs accepted?
Look: a spear head
X = A + B
everything is 1 but 0+0=0
accepts two inputs
what does a XOR gate look like?
what is the expression?
what is the truth table?
how many inputs accepted?
looks like a OR gate but with a line before it
X = A (+) B
0+0=0
0+1=1
1+0=1
1+1=0
accepts two inputs signals
what does a NAND gate look like?
what is the expression?
what is the truth table?
how many inputs accepted?
looks like a AND gate but with a circle at the end
X = (AB)’
everything is 1 but 1+1=10
accepts two inputs
what does a NOR gate look like?
what is the expression?
what is the truth table?
how many inputs accepted?
looks like a spear head with a circle at the end of it
X + (A+B)’
everything is zero but 0+0=1
accepts two inputs
how would you simplify
AB + BC + B’C
Solution
AB+ C(B+B’)
AB+C(1)
AB+C
how would you simplify
A’B + B’C’ + AB + B’C
1) A’B + B’C’ + AB + B’C
a. B(A’+A)+C(B’+B) distributive
b. B(1)+C(1) complment
c. Answer = B+C
how would you simplify
xy + xy′
a. xx+xy’+xx+yx commutative
b. x(y+y’+y) distributive
c. x(1+y) null elements
d. x(1) =identity
e. answer = x
how would you simplify
(x+y)(x+y′)
a. xx +xy’+yx+yy’ distributive
b. x+xy’+yx+0 idempotency and complement
c. x(y’+y) distributive
d. x(0) complement
e. answer = x
how would you simplify
(A+B)′(A′+B′)′
a. A’B’+AB de morgan law
b. A’A+B’+B communtative
c. 0+0 complement
d. Answer 0
what is a multiplexer?
Multiplexer (or MUX)
A circuit that uses a few input control signals to determine
which of several input data signals is routed to its output
signal
It is nothing but an electronic rotary switch!
