1. The Analytical Engine Hardware

2. 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.

3. 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).

4. 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!

5. The Gate Level The normally open switch. The normally closed switch. Truth tables for each.

6. Logic Any logical operation can be characterized by a combination of the operators and, or, and not. Review truth tables for each operator.

7. 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.

8. Logic Gates – And – Or – Not Construct circuits using expressions and tables. Given one, you should be able to construct the other two.

9. Logic AND Gate OR Gate NOT Gate Circuit – A collection of gates.

10. 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.

11. 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.

12. Binary Arithmetic - Addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10

13. 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

14. 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.

15. 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.

16. 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!

17. 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.

18. 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.

19. The End