Computer-Organization HOMEWORK 1- Approximate Average Solution

Homework Description
Please design a computational system whose transfer function is defined as follows. A series of 8-bit positive integer is generated as the input of the computational system by the test bench. The output value Y is a 10-bit positive integer, which is calculated according to equations (1), (2), (3) and (4).

𝑋 …………………………………………………………………………………….....(1)
,where Xi is the value of the ith input data and j>=1.
, n = 9 in this homework

𝑋𝑆 =
𝑋 , 𝑋 , 𝑋 … , 𝑋 ………………………………………………………………………...(2)
𝑋 𝑋 = 𝑋 , 𝑖𝑓 𝑋 ∈ 𝑋𝑆
= ……...(3)
𝑋 | (𝑋 ∈ 𝑋𝑆) 𝑎𝑛𝑑 𝑋 < 𝑋 𝑎𝑛𝑑 𝑋 − 𝑋 𝑖𝑠 𝑚𝑖𝑛𝑖𝑚𝑎𝑙 , 𝑖𝑓 𝑋 ∉ 𝑋𝑆

,where 𝑋 is the value of the jth approximate average
∑ ( )
𝑌 =…………………………………………………………………………........…..(4)
,where 𝑌 is the value of the jth output data.

The computational system produces the output sequence according to the given input sequence. Each input and output data in the respective sequence is indexed. This index, in terms of hardware, is the relative time when the input data is given or the output data is ready. Thinking as a hardware designer, the approximate average is chosen from the last n input data which should be stored in the system. The system should be able to calculate the integral part of the real average of the last n input data first. And then if the integral part of the real average equals to any one of the last n input data, the approximate average is simply the integral part. Else the approximate average is the one which is one of the last n input data whose value is smaller than and closest to the integral part of the real average. The above descriptions stated the desired operations as those defined by equations (1), (2), and (3).
After the approximate average is obtained, the output value can be calculated according to equation (4). First, the last n input value is added by the corresponding approximate average. And then they are summed up and divided by n-1. The output value is the quotient after division.
For example, assume that n=4, X1=3, X2=24, X3=16, X4=8, and X5=3. After the first 5 input items are given, the system should store them and calculate the output value. The average of the first 4 input values is 12(only the integral part is left). Since it is not in the set of {X1, X2, X3, X4}, the system selects one from {X1, X2, X3, X4} as the approximate average whose value is smaller than 12 and close to 12. In this case, the approximate average is 8. So the first output value is calculated n as
⌊[(3 + 8) + (24 + 8) + (16 + 8) + (8 + 8)] / [(4 - 1)]⌋ = 27 .
Similar to those described above, when the 5th input data item is given, the system should store X2, X3, X4 and X5 and calculate the corresponding output value. The 2nd output value should be the same as the first one because the values stored in the system is the same.

Design Specifications
a. Block Overview


b. I/O Interface
Signal Name I/O width Description
clk I 1 clock for the computational system
reset I 1 reset the state of the computational system when it asserts
X I 8 input data of the computational system
Y O 10 computed output

c. Timing Diagrams


d. File Description
File Name Description
CS.v RTL code for using Verilog
testfixture.v Test bench for verifying design
in.dat Input patterns
out_golden.dat Golden output patterns

Scoring
a. Functional Simulation (pre-sim) [100%]
All of the result should be generated correctly, and you will get the following message in ModleSim simulation. You can turn off the timing check in presim only??.











Appendix
(Hexadecimal number)
Index i Xi 𝑋 𝑋 Yj Index j
1 8f
2 0b
3 5d
4 20
5 f3
6 3e
7 e5
8 03
9 0c 5c 3e 056a 00ad 1
10 74 59 3e 054f 00a9 2
11 79 65 5d 06d4 00da 3
12 01 5b 3e 0561 00ac 4
13 30 5c 3e 0571 00ae 5
14 2e 46 3e 04ac 0095 6
15 a4 52 30 0494 0092 7
16 76 45 30 0425 0084 8
17 84 54 30 04a6 0094 9
18 51 5b 51 0614 00c2 10
19 d6 66 51 0676 00ce 11
20 70 65 51 066d 00cd 12
21 35 6b 51 06a1 00d4 13
22 10 68 51 0681 00d0 14
23 23 66 51 0676 00ce 15
24 e7 6e 51 06b9 00d7 16
25 3b 67 51 067e 00cf 17
26 6d 65 51 0667 00cc 18
27 34 61 3b 0584 00b0 19
28 61 54 3b 050f 00a1 20
29 89 57 3b 0528 00a5 21
30 bf 67 61 0708 00e1 22
31 dc 74 6d 0840 0108 23
32 d3 91 89 09ec 013d 24
33 9c 88 6d 08a5 0114 25
34 8f 92 8f 0a2b 0145 26




(Decimal number)
Index i Xi 𝑋 𝑋 Yj Index j
1 143
2 11
3 93
4 32
5 243
6 62
7 229
8 3
9 12 92 62 1386 173 1
10 116 89 62 1359 169 2
11 121 101 93 1748 218 3
12 1 91 62 1377 172 4
13 48 92 62 1393 174 5
14 46 70 62 1196 149 6
15 167 82 48 1172 146 7
16 118 69 48 1061 132 8
17 132 84 48 1190 148 9
18 81 91 81 1556 194 10
19 214 102 81 1654 206 11
20 112 101 81 1645 205 12
21 53 107 81 1697 212 13
22 16 104 81 1665 208 14
23 35 102 81 1654 206 15
24 231 110 81 1721 215 16
25 59 103 81 1662 207 17
26 109 101 81 1639 204 18
27 52 97 59 1412 176 19
28 97 84 59 1295 161 20
29 137 87 59 1320 165 21
30 191 103 97 1800 225 22
31 220 125 109 2112 264 23
32 211 145 137 2540 317 24
33 156 136 109 2213 276 25
34 143 146 143 2603 325 26


Figure 1. File hierarchy for homework submission

 You should finish all the requirements (shown below) in this homework and Project report.
 Verilog and SystemVerilog generators aren’t allowed in this course.
General rules for deliverables
 You need to complete this homework INDIVIDUALLY. You can discuss the homework with other students, but you need to do the homework by yourself. You should not copy anything from someone else, and you should not distribute your homework to someone else. If you violate any of these rules, you will get NEGATIVE scores, or even fail this course directly
 When submitting your homework, compress all files into a single zip file, and upload the compressed file to Moodle.
 Please follow the file hierarchy shown in Figure 1.
F740XXXXX ( your id ) (folder) src( folder ) * Store your source code
report.docx ( project report. The report template is already included. Follow the template to complete the report. )