Download The Analytical Engine

The Analytical Engine
Hardware
The Logic Machine
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Computers were originally wired to perform a
specific task.
The vision was a machine that could perform a task
without rebuilding the wiring.
Could the program itself control the flow of
electrons; turn circuits off and on by turning
switches off and on.
By connecting enough switches in the right ways,
the machine could perform any desired logical
operation.
The Gate Level
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Modern switches are about the size of a
bacterium!
Switch evolution:
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Electro-mechanical relays
Vacuum tubes
Transistors
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Emitter (out)
Collector (in)
Base (control)
Current applied to the base allows current to flow between
the collector and emitter (normally-open switch).
The Gate Level
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Printed-circuit technology allowed circuits to be
photographically printed on a non-conducting
board. Eventually the transistors, resistors,
capacitors, etc., were able to be
photographically imprinted too – integrated
circuits.
Photographs could be reduced in size so that
the imprinted circuits were only a few
molecules thick!
The Gate Level
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The normally open switch.
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The normally closed switch.
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Truth tables for each.
Logic
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Any logical operation can be characterized by
a combination of the operators and, or, and
not.
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Review truth tables for each operator.
Logic
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Notation
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Building Logical Expressions
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PQ means P and Q
P+Q means P or Q
P’ means not P
Q’ means not Q
See handout for rules
Practice building expressions and tables.
Logic
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Gates
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And
Or
Not
Construct circuits using expressions and
tables. Given one, you should be able to
construct the other two.
Logic
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AND Gate
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OR Gate
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NOT Gate
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Circuit – A collection of
gates.
Logic Gates
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Do Lab 7.1, 1a.-1f. Try
to place all 6 circuits on
the same board. Be
neat!
Do Lab 7.2. Place each
circuit on a separate
board and save as
instructed. Show each
circuit to your instructor
or S.A.
The Arithmetic Level
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Representing binary numbers
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Addition
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Off/on
High/low voltage
Link together 1-bit half-adders (see handout).
Carry-out of one becomes the carry-in of next.
Carry-in of low order adder is always zero.
Multiplication
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Shift left multiplies by 2.
Binary Arithmetic - Addition
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0+0=0
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0+1=1
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1+0=1
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1 + 1 = 10
Binary Arithmetic - Multiplication
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Multiplication
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0001 0101 = 21
Shift left = 21 * 2
0010 1010 = 42
More complex multiplication – 7 * 12
0
0 1
0 1 1
1 0 1
0
1
0
0
1
1
0
1
1
0
0
1
1 1
0 0
0 0
0
binary 7
binary 12
1 0 0
binary 84
Binary Arithmetic
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Complete Lab 7.3. Do
only steps 1 and 2.
Save your completed
circuit as directed.
Call your instructor or
S.A. to demonstrate your
half adder circuit.
Control Circuits
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Multiplexor – multiple inputs can be directed
to a single output depending on the condition
of a select line.
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Observe demonstration circuit (handout).
Decoder – a single input line can be directed
to multiple outputs depending on the condition
of a select line.
Storage
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Latch – memory circuit
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Forces the output to be the same as the data input
when current is applied to the strobe.
Removing current from the strobe causes the
output to remain unchanged.
The circuit “remembers” the data input value until a
new value is sent via the data input and current is
again applied to the strobe.
1 MB of memory would contain 2 million AND gates,
2 million NOR gates and 1 million NOT gates!
Toward Memory
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Complete Lab 7.4. Do
only Step 1 using the
Latch circuit provided on
the handout. Show your
circuit to your instructor
or S.A.
An Architect’s View
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Complete Lab 7.5. Do
Steps 1 – 6 only. Show
the results of Step 6 to
your instructor or S.A.
Be prepared to explain
how a single instruction
is executed as described
in Step 7.
The End