1007ICT Introduction to Computer Systems and Networks — Assignment 1 — Designing an 8 Function 4 Bit ALU

Pref­ace

Terms

You are view­ing an assign­ment from my 1007ICT Intro­duc­tion to Com­puter Sys­tems and Net­works course at Grif­fith Uni­ver­sity. This assign­ment is indi­vid­ual, in which intel­lec­tual prop­erty remains that of me, unless oth­er­wise stated via ref­er­enc­ing. Feel free to use or quote any mate­r­ial from this assign­ment, how­ever, you must credit this work as mine, and not rep­re­sent it as yours.

Def­i­n­i­tions

“Mine”, “me”, “I” all refer to Edmond den Dekker.
“You”, “yours” refers to any­one that has the abil­ity to view this con­tent in any way.

1. Cir­cuit Function

1.1. Brief

This 8 func­tion 4 bit ALU was cre­ated by com­bin­ing four 1 bit ALUs, each with the fol­low­ing com­po­nents and functionality–

• XOR
  • X = A XOR B
• AND
  • X = A AND B
• OR
  • X = A OR B
• Full Adder with Sub­trac­tion – Dou­bles as an Adder and Subtractor
  • X = A + B
  • X = A — B
• 4 Input Mul­ti­plexor – Pro­vides shift­ing left, right and thru capabilities
  • X = A Shifted left by 1 bit
  • X= A Shifted right by 1 bit
  • X = A

The above com­po­nents are located in a Logic Unit as seen in sec­tion 2.8. The Logic Unit is part of the 1 bit ALU. The logic unit’s out­put is selected via an 8 input mul­ti­plexor as shown in sec­tion 2.9. This allows the selec­tion of a par­tic­u­lar func­tion based on 3 bits. The design of the Shifter that is inside the Logic Unit, is more of a pas­sive design as Pin A of the Logic Unit is only cou­pled to Pin T of the 4 input mul­ti­plexor. The brunt of the Shifter func­tion­al­ity lies in the wiring of the 4 ALUs to make a 4 bit ALU as seen in sec­tion 1.2 below. The fol­low­ing sec­tions show the func­tion­al­ity of each com­po­nent of the 8 func­tion 4 bit ALU below.

1.2. 8 Func­tion 4 bit ALU

2. Cir­cuit Components

2.1. Full Adder

2.1.1. Cir­cuit Diagram

Full_Adder.dwm	Full_Adder.dwt

2.1.2. Truth Table

2.2. Full Adder with Subtraction

2.2.1. Cir­cuit Diagram

Full_Adder_With_Subtraction.dwm	Full_Adder_With_Subtraction.dwt

2.2.2. Truth Table

This cir­cuit utilises the Full Adder com­po­nent shown in sec­tion 2.1.1. When S is turned off (set to 0), this cir­cuit becomes the full adder shown in sec­tion 2.1.1. To avoid dupli­ca­tion, the truth table below will only show val­ues when S is turned on (set to 1).

2.3. 2 to 4 Decoder

2.3.1. Cir­cuit Diagram

Decoder_2_4.dwm	Decoder_2_4.dwt

2.3.2. Truth Table

The method­ol­ogy for cre­at­ing a 2 to 4 decoder was derived from http://​www​.cs​.uiuc​.edu/​c​l​a​s​s​/​s​p​0​8​/​c​s​2​3​1​/​l​e​c​t​u​r​e​s​/​0​7​-​D​e​c​o​d​e​r​s​.​ppt , accessed 22/​04/​2008. Although the schematic dia­gram was not shown in that source, I man­aged to imple­ment the func­tion­al­ity of turn­ing on and off this cir­cuit via a pin called EN. This aids in the cre­ation of a 3 to 8 decoder shown in sec­tion 2.4. The below truth table shows val­ues when EN is turned on (set to 1). If EN is turned off, this cir­cuit spits out no out­puts.

2.4. 3 to 8 Decoder

2.4.1. Cir­cuit Diagram

Decoder_3_8.dwm	Decoder_3_8.dwt

2.4.2. Truth Table

The method­ol­ogy for cre­at­ing a 2 to 4 decoder was derived from http://​www​.cs​.uiuc​.edu/​c​l​a​s​s​/​s​p​0​8​/​c​s​2​3​1​/​l​e​c​t​u​r​e​s​/​0​7​-​D​e​c​o​d​e​r​s​.​ppt , accessed 22/​04/​2008. By hav­ing a 2 to 4 decoder that can be switched on and off via pin EN, we can cou­ple 2 of these cir­cuits to make a 3 to 8 decoder. Below is the truth table for this cir­cuit.

2.5. 4 Input Selector

2.5.1. Cir­cuit Diagram

Selector_4.dwm	Selector_4.dwt

2.5.2. Truth Table

To list all pos­si­ble inputs for the above cir­cuit, a very large table would have to be pro­duced, one with 256 lines. There­fore I have decided to sim­plify the table and pro­vide more mean­ing. The truth table below shows that if A is on and if S1 is on, X will be on too. This pat­tern con­tin­ues for each let­ter input. The alphanu­meric input (the selec­tor), passes the value of its cor­re­spond­ing input to X. eg. To pass the value of C, you must turn on S3, that way X will be what ever C is. If the value of C is 0, and S3 is turned on, the value of C will still be passed to X, in which X will be 0.

2.6. 8 Input Selector

2.6.1. Cir­cuit Diagram

Selector_8.dwm	Selector_8.dwt

2.6.2. Truth Table

To list all pos­si­ble inputs for the above cir­cuit, a very large table would have to be pro­duced. There­fore I have decided to sim­plify the table and pro­vide more mean­ing. This cir­cuit works exactly like the one in sec­tion 2.5.1. The only dif­fer­ence with this one is that this selec­tor has 8 Inputs. Like the one in sec­tion 2.5.1, the truth table below shows that the Selec­tor (S1– S8) allows the value of the inputs (A– H) to be passed to X.

2.7. Mul­ti­plexor (3 to 8 Decoder & 8 Input Selector)

2.7.1. Cir­cuit Diagram

Multiplexor_3_8_Dec_8_Sel.dwm	Multiplexor_3_8_Dec_8_Sel.dwt

2.7.2. Truth Table

To list all pos­si­ble inputs for the above cir­cuit, a very large table would have to be pro­duced. There­fore I have decided to sim­plify the table and pro­vide more mean­ing. This Mul­ti­plexor allows us to input a 3 bit binary to use as a selec­tor of 8 pos­si­ble inputs (A – H)

2.8. Logic Unit (Log­i­cal AND/​OR/​XOR, Full Adder with Sub­trac­tion, Shifter)

2.8.1. Cir­cuit Diagram

Logic_Unit_8_Functions.dwm	Logic_Unit_8_Functions.dwt

2.8.2. Truth Table

To list all pos­si­ble inputs for the above cir­cuit, a very large table would have to be pro­duced. There­fore I have decided to sim­plify the table and pro­vide more mean­ing. The truth table below was con­structed on the basis that there are five com­po­nents which alto­gether make up 8 func­tions. All five com­po­nents are wired in par­al­lel. The light green sec­tions below show all pos­si­ble inputs and out­puts for each XOR, AND and OR com­po­nent. The cyan sec­tions show all pos­si­ble inputs and out­puts for the Full Adder in Sub­trac­tion mode (Sub set to 1), while the pale blue sec­tions show all pos­si­ble inputs and out­puts for the Full Adder in Addi­tion mode (Sub set 0). The cyan and pale blue sec­tions are a direct reflec­tion of sec­tions 2.1 and 2.2. The pur­ple sec­tions show all pos­si­ble inputs and out­puts for the 4 input mul­ti­plexor. When this com­po­nent is wired into a 4 bit ALU it becomes a func­tional 4 bit shifter as dis­cussed in sec­tions 1.1 and seen in sec­tion 1.2. The 4 input mul­ti­plexor shown 2.8.1 has an EN pin wired to a Vcc-​​, this just mean that power is being sent to that pin (ie. Set EN to 1), result­ing in the 2 to 4 decoder inside it to be turned on.

2.9. 1 Bit ALU (Logic Unit and Multiplexor)

2.9.1. Cir­cuit Diagram

ALU_1bit_8_Function.dwm

ALU_1bit_8_Function.dwt

2.9.2. Truth Table

To list all pos­si­ble inputs for cir­cuit dia­gram 2.9.1, a very large table would have to be pro­duced. There­fore I have decided to sim­plify the table and pro­vide more mean­ing. This cir­cuit utilises the logic unit and passes its value to X via the 8 input mul­ti­plexor. The 8 inputs of the mul­ti­plexor are selected depend­ing on the value of S1 to S3 pins. See sec­tion 2.8.1 for the logic unit’s truth tables. The light green sec­tions below shows all pos­si­ble inputs and out­puts when XOR, AND and OR func­tions are selected. The cyan sec­tions show all pos­si­ble inputs and out­puts for the Full Adder’s addi­tion func­tion. The pale blue sec­tions show all pos­si­ble inputs and out­puts for the Full Adder’s sub­trac­tion func­tion. The pur­ple sec­tions show all pos­si­ble inputs for when X becomes 1 and some pos­si­ble inputs for when X become 0. The pur­ple sec­tion is just a mul­ti­plexor in which it passes the value of A, L or R to X, depend­ing on the value for S1, S2 and S3.

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