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!
what does VLSI stand for
Very-large-scale integration - more than 100,000
what is a half adder?
A half adder is a basic binary addition circuit that adds two single-bit binary numbers (A and B) and produces two outputs: the sum (S) and the carry (C).
It doesn’t consider any carry input from previous additions.
The truth table for a half adder is as follows:
A B Sum (S) Carry (C)
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
what is a full adder?
A full adder is an extension of the half adder, and it can handle three inputs: A, B, and a carry input (C_in) from a previous addition.
It produces two outputs: the sum (S) and a carry output (C_out).
The truth table for a full adder is as follows:
A B C_in Sum (S) Carry Out (C_out)
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
