# MIT 6 189 - Building a processor from scratch (10 pages)

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## Building a processor from scratch

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## Building a processor from scratch

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Pages:
10
School:
Massachusetts Institute of Technology
Course:
6 189 - A Gentle Introduction to Programming Using Python
##### A Gentle Introduction to Programming Using Python Documents
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Optional Building a processor from scratch In this assignment we are going build a computer processor from the ground up starting with transistors and ending with a small but powerful processor The purpose of this assignment is to make you more familiar with the notion of logical circuits and the boolean functions which they implement It also illustrates the principle of modularity Starting with very simple transistor level circuits we will work our way up to a complete processor At each level of the processor design we will use the circuits that we have designed at the lower levels as black boxes ignoring their implementation details To aid in the clarity of your solution as well as the clarity of your thinking you should design your circuits modularly Once you have shown how to build a piece of circuitry such as an adder it is never again necessary to draw the details of its implementation simply use an appropriately labelled box to represent it Similarly you may wish to bundle parallel bunches of wires together into a single appropriately labelled n bit wide wire With these techniques you should be able to describe very complicated circuits with very simple and elegant circuit diagrams Note This is an optional assignment It was designed to help you understand the internal nature of a computer an important task for engineers and computer scientists alike Nothing but NAND The basic building block of our computer will be a two input NAND gate The truth table for a two input NAND gate is shown below The output z is 1 if and only if at least one of the two inputs x and y is 0 Which is the same as saying that the two outputs are not both 1 x y 0 0 0 1 1 0 1 1 z x y 1 1 1 0 As we shall see below any other gate can be constructed using nothing but NAND gates Because of this we say that NAND gates are complete It is interesting to note that not all gates have this property for example AND gates are incomplete that is there is no way to construct all the other gates using only AND gates A NAND gate is drawn schematically as shown below x z y For this assignment the NAND gate is the lowest level you ever need to worry about However for the curious we will include a little information about how gates are actually built from transistors In particular we will use Complementary Metal Oxide Semiconductor CMOS transistors one of the several di erent types available A NAND gate can be implemented in CMOS using four transistors as shown below The horizontal line at the very top of the gure represents a high voltage value Vdd say 5 volts while the three horizontal lines at the bottom of the gure represent the ground voltage 0 1 volts The high voltage value represents a binary 1 while the low voltage value represents 0 The inputs x and y are each connected to the gates of two transistors A transistor is basically a door Each of the bottom two transistors in this gure is open when the voltage on its gate is high and closed when it is low Each of the top transistors is open when the voltage on its gate is low and closed when it is high When either of x or y is 0 the path from the ground to the output z is closed but at least one path from Vdd to z is open so z takes on the high voltage When both x and y are one there is no path from Vdd to z but there is a path from the ground to z so z takes on the low voltage vdd z x y ground Problem 0 5 points Using a NAND gate as your basic building block show how to construct circuits that perform the following functions NOT AND OR and XOR You should not draw any transistors begin with the NAND gate schematic You may design the circuits in any order that you want and once you have designed a circuit you may use it in the construction of other circuits using the appropriate schematic The truth tables for these functions along with their schematics are shown below 1 NOT gate x 0 0 1 1 z x 1 1 0 0 x z 2 AND gate x y 0 0 0 1 1 0 1 1 z x y 0 0 0 1 x z y 3 OR gate x y 0 0 0 1 1 0 1 1 z x y 0 1 1 1 x z y 2 4 XOR gate x y 0 0 0 1 1 0 1 1 z x y 0 1 1 0 x z y Building an adder Problem 1 8 points Now that you have designed a collection of useful gates you can use them to construct more sophisticated circuits Using your collection of gates draw a circuit that implements 4 bit grade school addition which should be able to do calculations like 0110 0100 1010 You do not need to deal with over ow for example 0110 1100 0010 is OK You should proceed by rst constructing a 1 bit adder that takes as input two bits and outputs a sum bit and a carry bit e g adding 0 and 1 produces sum 1 and carry 0 where as 1 and 1 produces sum 0 and carry 1 Then show how to combine 1 bit adders to construct a 4 bit adder 3 Multiplexers and Demultiplexers Two types of circuits will come in very handy as we design our processor multiplexers and demultiplexers Intuitively a multiplexer mux takes a binary number n and selects the nth one of its inputs to forward on A demultiplexer demux takes a number n and sends its input out on the nth output line y00 x00 y01 x01 y x x10 y02 x11 y03 a0 a1 a0 a1 Figure 1 At left a four way one bit mux At right a four way one bit demux The schematic for a 4 way 1 bit mux is shown in Figure 1 Left It has four data inputs x00 x01 x10 x11 two control inputs a0 a1 and one output y The value of y is equal to the input speci ed by the binary number a0 a1 i e y xa0 a1 As an example if x00 1 x01 1 x10 0 x11 1 and a0 a1 10 then y x10 0 A mux is also called a selector because the control lines select from among the possible inputs The schematic for a 4 way 1 bit demux is shown in Figure 1 Right This circuit has a 1 bit data input x a 2 bit control input a0 a1 and 4 1 bit outputs y00 y01 y10 y11 A demux works as follows The value of x is transferred to the output line speci ed by a0 and a1 i e ya0 a1 x The value on all of the other outputs …

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