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COMP1007 Computer Fundamentals - LargeCoursework01: CPU

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UKUniversity of ManchesterCOMP1007Computer FundamentalsCPU



Throughout COMP1007, we’ve looked at how we can build a CPU from raw digital logic. In this coursework, we’ll put some of the building blocks we have already built together to build some of the major building blocks that you might find in a simple CPU1 using the nand2tetris hardware simulator and hardware description language. CourseNana.COM

This coursework is split into four sections. In the first section, you will create a series of combinatorial logic gates that will be used by the later parts of the systems. In the second section, you’ll build a simplified version of the Z80 ALU. CourseNana.COM

In the third section, you will build some sequential logic gates that are used by the final section, where you will integrate the gates you have created in the previous sections to form a simplified section of the Z80 CPU. It is intended that in each section you will make use of the gates supplied, alongside any gates you create as part of the exercise, and the standard gates provided as part of nand2tetris (e.g And, Or, Not, Mux, Bit, etc.) CourseNana.COM

This document outlines how the coursework is assessed, and descriptions of the various logic circuits to be built, along with some tips on how to implement them. This coursework is worth 20% of your final COMP1007 mark, and will be given a mark out of 40. As ever, a mark of 40% (i.e. a mark greater than 16) or above is a pass mark for this coursework. CourseNana.COM

Good luck… You will almost certainly nd it impossible to complete these exercises unless you have read the relevant chapters of the book ‘The Elements of Computing Systems: Building a Modern Computer From First Principles’ — the book which accompanies nand2tetris. CourseNana.COM

Implementation Detail Inside the git repository, you forked and cloned via git in the usual fashion, you will find skeleton .hdl files and test scripts for each of the components you need to implement. It is strongly recommended that you use these skeleton otherwise your implementation may not work against the marking test scripts. CourseNana.COM

1 This CPU is inspired by the classic 8-bit Z80 CPU. The Z80 CPU was very popular in the late-1970s and 1980s and was the brain of many CourseNana.COM

In this first section, we are going to build various combinatorial logic circuits that are used in parts of the CPU. If you have already completed the lab exercises then you will have built similar components already, so will be able to adapt them for this exercise. Some of them, however, are new and might require a bit of thought… There are five support components that you need to implement. The five logic chips you are to implement are: CourseNana.COM

Gate Description
Mux4 This has two input buses, a and b and one output bus, out. Alsopresent is a sel input, which is used to select whether input a or b is passed to out. If sel is false, input a should be selected, otherwise input b should be selected. Note: You can assume that the single bit Mux is defined on the system already and takes three inputs, a, b and sel, and produces an output out.
Mux8 This is an 8-bit version of Mux4. It has two input buses, a and b and one output bus, out. Also present is a sel input, which is used to select whether input a or b is passed to out. If sel is false, input a should be selected, otherwise input b should be selected. Note: You can assume that the single bit Mux is defined on the system already and takes three inputs, a, b and sel, and produces an output out.
Mux4Way8 This is essentially the same a the Mux8 except it can select between four different inputs (a, b, c, and d) and so sel is two bits wide — hence, 4Way… Hint You should be able to build this using your implementation of Mux8
Mux8Way8 This is essentially the same as the Mux4Way8 defined above, however this time there are eight inputs and sel is three bits wide. You should adapt your earlier implementation to reflect this change.
HiLoMux This has one 8-bit input bus, in, and one 4-bit output bus, out. Also present is a sel input, which is used to select what appears on out. If sel is false, then out should contain the lower 4-bits of in (i.e. in[0], in[1], in[2], in[3]). If sel is true, then out should contain the upper 4-bits of in (i.e. in[4] mapped to out[0], in[5], mapped to out[1], etc.). In other words, the HiLoMux can be used to select a nibble from a byte… We’ll use this circuit in a later exercise to enable the 4-bit ALUcore below to do 8-bit operations.

Note only Mux4 and HiLoMux are required to complete later parts of this coursework. CourseNana.COM

02 Arithmetic and Logic Unit

In lab exercise three, you created a series of gates that could process 8-bit values (Not8, And8, Or8, Mux8, etc.) while in lab exercise one you created a single gate, (Add4C) which could add two 4-bit numbers together. In this exercise, you will combine these gates together to form the Arithmetic and Logic Unit (ALU) for an 8-bit CPU. This ALU is based on the ALU in the Z80 microproccessor, and is much simpler to understand than the nand2tetris ALU we considered in the online session on the 26th October. Test scripts are supplied to enable you test whether your implementation is correct, don’t worry if you didn’t complete lab exercise one or three — the git repository contains implementations of all the gate you need to use for this exercise (Details of the supplied gates can be found in Appendix A). CourseNana.COM

In this section, you will implement our simplified Z80 Arithmetic and Logic Unit, or ALU2. A skeleton file ALUcore.hdl is provided as a starting point. The core of our simplified Z80 ALU is represented pictorially below and consists of two 4-bit inputs, A and B, a 4-bit output and carry inputs and outputs. Even though this ALU is only 4-bits wide, it is still able to perform 8-bit computations as we will see in section four. CourseNana.COM

The ALU also has a series of control inputs, which can be used to select what function the ALU performs and some outputs that are linked up to other sections of the CPU. These control inputs and outputs are described below. CourseNana.COM

You may find it helpful to read the chapter on ‘Boolean Arithmetic’ in the nand2tetris book (available online)for more information about designing an ALU, although the one we’ll implement here is simpler. CourseNana.COM

The inputs a and b along with the output, out, are multi-bit, and so we represent them in the HDL as buses. A bus is just a collection of logic signals that we keep together (in this case they reach represent a numeric value in binary). We can define them in the HDL by suffixing the pin name with square brackets, thus: a[4]. This denotes that a is a bus 4-bits wide, numbered 0–3. Each individual bit can be accessed by placing the number of the required bit in the square brackets. So a[3] would access the fourth bit (remember, numbering starts from zero!) from the right. Again, re-read the relevant sections of nand2tetris for more details on the HDL syntax. CourseNana.COM

The four control signals, sums, ands, xors, and ors, are used to control the output produced by the ALU by selecting between the output of the four possible functions it can perform. These are used to select3 whether the two inputs are Add-ed, And-ed, XOR-ed, or OR-ed together respectively — each of these can be produced using the components supplied. CourseNana.COM

You can assume that only one control signal will be active at a time, and so the order you select between the possible outputs doesn’t matter. The carryIn input of the ALUcore should be connected to the carryIn of your Add4C, while the carryOut signal of the ALUcore should be connected to the carryOut of your Add4C when adds is true, otherwise it should be false. This completes the implementation of our ALU’s core — in the final section, you will build some more logic to drive the core, enabling it to perform subtraction as well as addition, and also to be able to perform 8-bit operations. CourseNana.COM

Remember this is hardware, so we perform all the operations and select the desired output… CourseNana.COM

Various test scripts are provided for the ALUcore (ALUcore-add.tst, ALUcore-and.tst, etc.) which can be used to test each of these individual cases Successfully completing parts one and two will give you a passing grade for this exercise… CourseNana.COM

The components you will build in this section are similar to Register8 in lab exercise two and you can assume the Bit logic gate is available for you to use. Chapter 3 of the nand2tetris book also contains detailed descriptions of some related circuits. CourseNana.COM

04 ALU Data Path CourseNana.COM

The Z80 CPU is an 8-bit CPU but it was implemented using a 4-bit ALU. This meant that it had to perform 8-bit maths as a sequence of two operations first on the low 4-bits of the data, then on the high 4-bits of the data, propagating any carry as necessary. In this section, you are going to implement similar logic. The three gates in this section wrap up a single 4-bit ALUcore that you implemented in the second section and provides the additional logic needed to enable it to perform 8-bit operations. Operationally, these gates will work as if they had two ALUcores connected in parallel with the carryOut of the first linked to the carryIn of the other but, instead of using two ALUcores, ALUDataPath will perform the selected operation as a sequence of two operations one after the other using a single ALUCore: first, on the lower 4-bits, or nibble4, of the 8-bit values, and then secondly, perform the same operation on the high nibble of the 8-bit value — preserving any carry value from the first operation and feeding back into the second operation. There are three gates to implement for this section. The first gate, ALUChopper, takes in 8-bit values, stores them and enables us to chop them into the 4-bit nibbles necessary to perform the calculation. The second gate, ALUProcess, then uses the two 4-bit nibbles from the first gate to perform an 8-bit calculation using a single 4-bit ALUcore and produce an 8-bit output. Finally, the last gate ALUDataPath, just wraps up the first two into an easy to use package. CourseNana.COM

ALUChopper This logic gate is used to both store the two 8-bit values required for the computation by the ALU and also to chop the stored values into two 4-bit values that can then be fed into the ALU. This gate onlyhas a single 8-bit input, in which is used to provide the 8-bit input values. The values for the ALU will be provided in sequence, and so two further inputs aLoad and bLoad are used to select whether the value on in should be stored ready to be used for the a input or b input to the ALUcore. The logic gate has two 4-bit outputs, aHiLo (which should contain the value stored when aLoad is true) and bHilLo (which should contain the value stored when bLoad is true) which are used to provide 4-bit outputs ready for ALUProcess. To select whether these contain the the high nibble, or the low nibble of the output there is a final input hiLo which switches between them. If hiLo is CourseNana.COM

4-bit binary values are referred to as a nibble — because they are half a byte… The lower nibble, would there for be be bits 0-3 of a byte, and the higher nibble be bits 4-7. CourseNana.COM

true, then aHiLo and bHiLo contain the upper nibble, otherwise if hiLo is false, they contain the lower nibble. CourseNana.COM

ALUProcess ALUProcess wraps up a single 4-bit ALUcore, and enables it to perform 8-bit computations (sequentially). This is done by using that ALUcore to compute the lower nibble (bits 0—3) first, and storing the result in part of a register, and then performing the same calculation on the high nibble (bits 4—7) and storing that part of the computation in the same register. For boolean operations (And, Or, Xor), this alone will produce the correct result but for addition we need to go one step further since we need to ensure that the carry produced by the first half of the computation is stored and then fed back into the ALUcore (via carryIn) for the second half of the computation). In addition, we will also need to store the carryOut bit when we update high nibble of the result to ensure it updates the output at the same time as the rest of the computation. Several of the inputs to this chip are familiar: sums, ands, xors, and ors are used to select the operation that the ALUcore will perform and so can be wired directly to the equivalent inputs on the single ALUcore in your solution. The inputs a and b are used to provide the input to ALUcore (they’ll be connected to the ALUChopper above to select the correct bits at the correct time), and again can be connected directly to ALUcore. The other inputs and outputs need a little more explanation. The input hiLo is straight-forward and, as with ALUChopper, is used to select whether ALUcore is working on the high (hiLo=true) or low (hiLo=false) nibble of the computation. You will need to use this (in combination with some of the other inputs to ensure the correct part of the chip operates). The output, out, contains the result of the calculation performed by the ALUcore. However, since ALUcore will need to perform two sequential operations to build up the result, you will need to use a register to store the high and low nibbles of the result as they are calculated separately… The input resLoad is used to tell this register when to store the output of the ALUcore and should be combined with hiLo to select which nibble is updated. When the relevant operation is performed on the high nibble, the carryOut bit from the ALUcore should also be stored before being presented to the ALUDataPath’s carryOut. Hint: Remember, you’ll need to preserve the carryOut Bit from the ALUcore when it performs the operation on the lower nibble. CourseNana.COM

ALUDataPath The final gate, ALUDataPath, ties the other two together to form a usable system. Most of its inputs can be directly connected to the equivalent input on ALUChopper and/or ALUProcess. The inputs op1Load and op2Load are used to specify whether dataIn contains the first or second operand for the computation and so can be used to drive aLoad and bLoad respectively CourseNana.COM

on the ALUChopper. In addition, the aHiLo output of ALUChopper can be connected to the a input of ALUProcess. The final input, notOp2, is necessary to enable the ALU to perform a subtraction. It used to select whether the second input (b) to ALUProcess is inverted (i.e. fed through a Not4) or not. If notOp2 is true, then ALUProcess should be fed the inverted version. By inverting the second operand, and setting carryIn to be 1, we can get the ALU to subtract by adding the negative version of a number (remember, the two’s complement representation is formed inverting and adding one…). Once again, a test script is provided in the repository to enable you to ensure that your implementation is working correctly. However, it’ll probably worth trying the circuit out ‘by hand’ so you get an idea how it works. Appendix B describes how the ALUDataPath can be driven to perform a calculation. CourseNana.COM

DataPathDriver The pipeline will also award an additional five marks if your ALUDataPath works under the control of the supplied DataPathDriver to correctly perform calculations (you can test this yourself by running the provided DataPathDriver.tst test script in nand2tetris). CourseNana.COM

Several logic gates are provided for you as part of the git repository and it is expected that you will make use of these in your solution. Details of the gates provided are given below. In addition, should you need to, you can make use of any of the gates we have already seen, such as And, Or, Xor, Not, Mux, Bit, FullAdder, HalfAdder, etc. CourseNana.COM

Not4 CourseNana.COM

This has one input bus, in, and one output bus, out. Each bit of the output is the inverse (i.e. not) of the corresponding input bit. CourseNana.COM

And4 CourseNana.COM

This has two input buses, a and b, and one output bus, out. Each bit of the output is the result of logically anding together the corresponding input bits in a and b. CourseNana.COM

Or4 CourseNana.COM

This has two input buses, a and b, and one output bus, out. Each bit of the output is the result of logically oring together the corresponding input bits in a and b. CourseNana.COM

Xor4 CourseNana.COM

This has two input buses, a and b, and one output bus, out. Each bit of the output is the result of logically Xoring together the corresponding input bits in a and b. CourseNana.COM

Add4C CourseNana.COM

This has two input buses, a and b, and one output bus, out. Each bit of the output is the result of adding together the corresponding input bits in a and b, while making sure that any carry is propagated to the next bit. Add4 also has an additional carryIn input, which is used to feed carry into first addition, and a carryOut output which carries the carry out of the final addition. This gate has one 8-bit input bus, in, and one output bus, out, and is designed to store a single byte (8-bits) of information. As with pre-supplied Bit, a further input load controls whether the output should be updated to reflect the new input value (when true), or should preserve the output. CourseNana.COM

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