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The Analytical Engine Hardware
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The Logic Machine 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.
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The Gate Level Modern switches are about the size of a bacterium! Switch evolution: – Electro-mechanical relays – Vacuum tubes – Transistors Emitter (out) Collector (in) Base (control) Current applied to the base allows current to flow between the collector and emitter (normally-open switch).
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The Gate Level 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!
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The Gate Level The normally open switch. The normally closed switch. Truth tables for each.
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Logic Any logical operation can be characterized by a combination of the operators and, or, and not. Review truth tables for each operator.
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Logic Notation – PQ means P and Q – P+Q means P or Q – P’ means not P – Q’ means not Q Building Logical Expressions – See handout for rules Practice building expressions and tables.
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Logic Gates – And – Or – Not Construct circuits using expressions and tables. Given one, you should be able to construct the other two.
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Logic AND Gate OR Gate NOT Gate Circuit – A collection of gates.
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Logic Gates 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.
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The Arithmetic Level Representing binary numbers – Off/on – High/low voltage Addition – 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 – Shift left multiplies by 2.
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Binary Arithmetic - Addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10
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Binary Arithmetic - Multiplication Multiplication – 0001 0101 = 21 – Shift left = 21 * 2 – 0010 1010 = 42 More complex multiplication – 7 * 12 0 1 1 1 binary 7 1 1 0 0 binary 12 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 binary 84
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Binary Arithmetic 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.
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Control Circuits Multiplexor – multiple inputs can be directed to a single output depending on the condition of a select line. – Observe demonstration circuit (handout). Decoder – a single input line can be directed to multiple outputs depending on the condition of a select line.
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Storage Latch – memory circuit – 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!
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Toward Memory 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.
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An Architect’s View 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.
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The End
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