Unformatted text preview: Chapter 4: Gates and Circuits
Chapter The following Boolean operations are easy to incorporate
The
into circuitry and can form the building blocks of many
more sophisticated operations…
more
The NOT Operation (i.e., what’s the opposite of the operand’s value?)
NOT 1 = 0 NOT 0 = 1 NOT 10101001 = 01010110
NOT 00001111 = 11110000 The AND Operation (i.e., are both operands “true”?)
1
AND 1
1 1
AND 0
0 0
AND 1
0 0
AND 0
0 10101001
AND
AND
10011100
10011100
10001000 00001111
AND
AND
10110101
10110101
00000101 The OR Operation (i.e., is either operand “true”?)
1
OR 1
1 1
OR 0
1 0
OR 1
1 0
OR 0
0 10101001
OR 10011100
10111101 00001111
OR 10110101
10111111 Chapter 4
Gates and
Gates
Circuits
Circuits
Page 1
Page More Boolean Operators
More
The NAND Operation (“NOT AND”)
1
NAND 1
0 1
0
0
NAND 0 NAND 1 NAND 0
1
1
1 10101001
NAND 10011100
01110111 00001111
NAND 10110101
11111010 The NOR Operation (“NOT OR”)
1
NOR 1
0 1
NOR 0
0 0
NOR 1
0 0
NOR 0
1 10101001
NOR 10011100
01000010 00001111
NOR 10110101
01000000 The XOR Operation (“Exclusive OR”, i.e, either but not both is “true”)
1
XOR 1
0 1
XOR 0
1 0
XOR 1
1 0
XOR 0
0 10101001
XOR 10011100
00110101 00001111
XOR 10110101
10111010 Chapter 4
Gates and
Gates
Circuits
Circuits
Page 2
Page Transistors
Transistors Transistors are relatively inexpensive mechanisms
Transistors
for implementing the Boolean operators.
for
In addition to the input connection (the base)
In
base
Transistors are connected to both a power source
and a voltage dissipating ground.
and Essentially, when the input voltage is high, an electric
Essentially,
path is formed within the transistor that causes the power
source to be drained to ground.
source
When the input voltage is low, the path is not created,
When
so the power source is not drained.
so Chapter 4
Gates and
Gates
Circuits
Circuits
Page 3
Page Using Transistors to Create Logic
A NOT gate is essentially
NOT ates
Gatesa transistor all by
G
implemented by
itself.
itself.
A NAND gate uses a slightly more complex
NAND
setup in which both inputs would have to
both
be high to force the power source to be
grounded.
grounded.
Use the output of a NAND gate as the input
Use
to a NOT gate to produce an AND gate,
to
A NOR gate grounds the power
NOR
source if either or both of the inputs
are high.
are
Use the output of a NOR gate as the
Use
input to a NOT gate to produce an OR
gate..
gate.. Chapter 4
Gates and
Gates
Circuits
Circuits
Page 4
Page How to Use Logic Gates for
ANDs and ORs are all well and good, but how can they be
ANDs
Arithmetic
Arithmetic
used to produce binary arithmetic?
used
Let’s start with simple onebit addition (with a “carry” bit
Let’s
just in case someone tries to add 1 + 1!).
just
0
0
1
1 +
+
+
+ 0
1
0
1 =
=
=
= Sum Carry
Bit
Bit
0
0
1
0
1
0
0
1 0
0
1
1 XOR
XOR
XOR
XOR 0
1
0
1 =
=
=
= Result
0
1
1
0 0
0
1
1 AND
AND
AND
AND 0
1
0
1 =
=
=
= Result
0
0
0
1 Notice that the sum bit always yields the same result as
Notice
the XOR operation, and the carry bit always yields the
same result as the AND operation!
same
By combining the right circuitry, then, multiplebit
By
addition can be implemented, as well as the other
arithmetic operations.
arithmetic Chapter 4
Gates and
Gates
Circuits
Circuits
Page 5
Page Memory Circuitry
Memory
With voltages constantly on the move, how can a piece of
With
circuitry be used to retain a piece of information?
retain
In the SR latch, as long as the S and
In
R inputs remain at one, the value of
the Q output will never change, i.e.,
the circuit serves as memory!
the
To set the stored value to one, merely set the S input to
To set
zero (for just an instant!) while leaving the R input at one.
zero
To set the stored value to zero, merely set the R input to
To
zero (for just an instant!) while leaving the S input at one.
zero
Question: What goes wrong if both
Question:
both
inputs are set to zero
simultaneously?
simultaneously? Chapter 4
Gates and
Gates
Circuits
Circuits
Page 6
Page Integrated Circuits
Integrated
How does all of that elaborate circuitry get placed on the
How
tiny microchips used in modern computers?
tiny A clean silicon
clean
wafer is oxidized to
produce a thin layer
of silicon dioxide,
which is then
coated with a
radiationsensitive
film.
film. The areas
The
covered by
silicon dioxide
remain
positively
charged. The
silicon dioxide
is removed
is The wafer is
The
masked by
lithography to
expose it
selectively to
ultraviolet light,
which causes the
film layer to
become
dissolvable.
dissolvable. The wafer is
The
oxidized again.
oxidized Lightexposed
Lightexposed
areas are
dissolved,
exposing parts of
the silicon dioxide
layer, which are
removed by an
etching process.
etching An opening is
An
etched down to the
positively charged
silicon using a
reverse mask.
reverse The remaining film is
The
removed in a liquid bath.
The areas of silicon
exposed by the etching
process are negatively
charged by exposure to
either arsenic or
phosphorus vapor at high
temperatures
temperatures Another oxidation
Another
cycle forms a thin
layer of silicon
dioxide on the
positively charged
region of the wafer.
region Windows are
Windows
etched in the
negatively charged
silicon areas in
preparation for
metal deposits.
metal Chapter 4
Gates and
Gates
Circuits
Circuits
Page 7
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 Fall '08
 Klein,S
 Computer Science, Logic gate

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