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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.)

Operation of a Latch

• To store a bit d:1. Set strobe=1.2. Set input=d. This also sets output=d.3. 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.

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.

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.

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.