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The Logic Machine

The Logic Machine. We looked at programming at the high level and at the low level. The question now is: How can a physical computer be built to run a program? In this module, we look at computer hardware and how it can be made to execute a program.

jared-summers
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The Logic Machine

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  1. The Logic Machine • We looked at programming at the high level and at the low level. • The question now is: How can a physical computer be built to run a program? • In this module, we look at computer hardware and how it can be made to execute a program. • In the early days of computing, a computer was hard-wired to perform a specific task. • A conceptual leap was that a program could be stored in memory along with other data.

  2. The Big Switch • Modern electronic digital computers are based on simple switches---lots of them. • Switches come in a variety of forms: a light switch, an electromechanical relay, a vacuum tube, a transistor. • By connecting enough switches in the right way, a computing machine can be constructed to perform any logical operation you want. • Integrated circuits consisting of transistors and other electronic components are constructed photographically. Photographs can be reduced in size to construct very small integrated circuits.

  3. Anatomy of a Switch • A switch consists of three parts: an “in”, an “out”, and a “control”. Think of a light switch. • Normally open switch. Truth table. • Normally closed switch. Truth table. • You don’t have to think of a switch as being an electrical switch. • A switch can control the flow of water or the flow of traffic or the rotation of mechanical gears or any of a number of things. • …which brings us to the viewpoint of thinking of switches as controlling the flow of logic.

  4. Logic • It is known that any logical expression can be generated from only three basic logical operators. • AND - “P and Q” is denoted PQ. Truth table. • OR - “P or Q” is denoted P+Q. Truth table. • NOT - “not P” is denoted P’. Truth table. • Example of how a more complicated logical expression can be built from the three basic operators. • Since P+Q=(P’Q’)’, we can get rid of OR and reduce the number of basic logical operators to only two---namely, AND and NOT.

  5. Gates • To build a computer which can carry out logical expressions, “all” we have to do is design circuit analogs of AND, OR, and NOT. • The circuit analogs of AND, OR, and NOT are called the AND gate, the OR gate, and the NOT gate. • The Logg-O program.

  6. Gates • Since OR can be written in terms of AND and NOT, we need to build circuit analogs only for AND and NOT. • This can be done with simple switches. • Once we can build gates from switches, we can build any logical expression from the basic gates. • Think of the basic gates as “building blocks”. • circuit - a collection of gates.

  7. Gates • Examples: • A one-bit comparator. This is the example we used to illustrate how to build a more complicated logical expression from the three basic operators. • A one-bit half adder. This adds two bits (0 or 1) and produces their sum along with a carry. • A one-bit full adder. This is constructed from two half adders and includes provision for a carry in. • Several one-bit full adders can be hooked together to add longer strings of bits.

  8. On to Arithmetic • To handle longer strings of binary bits, we can enter the data in serial or in parallel. • Example: 37 in binary is 100101. In serial, 100101 would be input on one line one digit at a time. Each digit corresponds to an electrical pulse--high, low, low, high, low, high. Similar to Morse Code. Simple, but slow. In parallel, we decide in advance how many digits our computer will use for numbers and assign a separate line to each digit. 100101 requires 6 lines. More complex, but fast.

  9. Addition • As noted, addition of longer strings of bits is done by combining one-bit adders. • For example, an adder which adds two 4-bit numbers input in parallel is constructed from four one-bit adders. • Multiplication is a bit more complicated, but is essentially addition with shifting. • By combining these basic building blocks in ever more complex ways, circuits can be designed to perform all the operations associated with modern computers.

  10. Control • Now that we know (more or less) how to build computer circuits, how do we control them? That is, how do we program a computer? • The trick is to design a computer so that, every time it has to perform an operation, it performs ALL operations and lets a program set switches to determine which result to use. • This is done using a multi-way switch called a multiplexor. • Example: A two-way multiplexor (MUX) which determines whether the output is a or b.

  11. Control • Multiplexors can be combined to build an arithmetic-logic unit (ALU). • An ALU simultaneously performs all possible operations on its inputs. The result that is chosen by the select line is the output. • Example: A two-function two-bit ALU to perform addition a+b and multiplication ab. • A decoder is the reverse of a multiplexor. It sends its input to one of many possible output lines depending on the value of the select line. • Example: A four-way decoder.

  12. Storage • Finally, we need to add storage capability to a computer to remember processed information. • To add memory, we use a latch. • latch - a circuit that can store a single 0 or 1. • A latch can be constructed in a number of ways using gates. • Example: A latch constructed from two AND gates, a NOT gate, and two NOR gates. (You looked at the NOR gate in Lab 7.2.)

  13. Operation of a Latch • To store a bit d: • Set strobe=1. • Set input=d. This also sets output=d. • Set strobe=0. • As long as strobe=0, output=d. • To change the stored value, repeat steps 1, 2, and 3. • Thus, the latch “remembers” the value d until a new value of d is sent with strobe=1.

  14. Memory • Gates and latches can be used to build memory. • 1 MB of memory contains about 75 million gates! • 64 MB of memory contains about 4.8 billion gates.

  15. Architecture • We now have a collection of basic building blocks for computers. • Switches -----> gates -----> arithmetic logic unit and memory. • How these building-block components are combined to construct an actual computer is called architecture. • architecture - that which is visible to the assembly language programmer. • High-level programmers don’t have to worry how a computer is put together; assembly language programmers do.

  16. Fetch-Execute Cycle • To keep a computer operating in an orderly fashion, a computer needs an internal clock. • The ticks of a computer clock are measured in millions of cycles per second (Hertz). • Example: A 500 MHz computer has a clock operating at 500 million Hertz. • At one tick of the computer clock, the computer fetches an instruction from memory. • At the next tick, the computer begins to execute the instruction. • At subsequent ticks, the computer finishes executing the instruction, fetches the next instruction, executes it, and so on.

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