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ECE 6913 in binary

Creation date：2024-05-08 14:54:19

Belonging category：计算机computer science

Tag ECE 6913

in binary

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ECE 6913 INET Quiz 1 Solutions

1. Assume a 10-bit floating point representation format where the Exponent Field has 4 bits and the
Fraction Field has 5 bits and the sign bit field uses 1 bit

a. What is the representation of -8.80158 x 10-2 in this Format (in binary:
-0.00010110100010000011 )
[assume:
bias = 2N-1 - 1= 24-1 -1= 7 (where N = number of exponent field bits) for normalized
representation, and 1-bias = -6 = bias for denormalized representation]. What
10-bit pattern represents the number −0.125 = −1/8? What base-10 integer or fraction does this
10-bit floating point representation format of 0101001001 equal to?

• normalizing,
-8.80158 x 10-2 = -1.0110100010000011 x 2-4

val(exp) = exp field – bias
exp field = -4 + 7 = + 3 = 0011
Fraction field = 01101

-1.01101 x 2-4
= 0.087890625 = 8.7890625 x 10-2
ratio of represented number to actual value
= 0.087890625 / 0.0880158 = 0.9974239
error = 1- 0.9974239 = 0.002576 = 0.2576 %
• -0.125 = -0.001002 = -1.002 x 2-3
S = 1
F = 00100
val(exp) = exp field – bias = -3 = exp field – 7 => exp field = 4
E = 0100

Exponent Field: 4 bits Fraction Field: 5 bits S
0011 01101 1
0100 00000 1
• 10 bit floating point representation of 0101001001 :

E = 10102; exp field = 10decimal; F = 01001
So, val(exp) = 10 – 7 = 3
1.01001 x 23
= 1010.012 = 10.2510
b. What is the range of representation for positive normalized numbers – what is the largest and smallest
normalized number represented in this format? What is the range of representation for positive
denormalized numbers? – what is the largest and smallest denormalized number represented in this
format?
• Normalized Numbers:
Maximum value represented: val (exp) = exp field – bias = 14 – 7 = 7
= 1.11111 x 27 = 28 – 0.00001 x 27 = 256 – 2-5 x 27 = 256 – 4 = 252

Minimum value represented: val (exp) = exp field – bias = 1-7 = -6;
fractional field = 00000
1 x 2-6 = 0.015625

Range: 0.015625 → 252
• Denormalized numbers:
Maximum value represented: val (exp) = 1 – bias = – 6
= 0.11111 x 2-6 = = 2-6-0.00001 x 2-6 = 2-6 – 2-11
= 0.015625 - 0.000488281250 = 0.01513672

Minimum value represented: val (exp) = 1 – bias = – 6
= 0.00001 x 2-6 = = 2-5 x 2-6 = 2-11 = 0.00048828125

Range = 0.00781250 → 0.00048828125
1010 01001 0
1110 11111 0
0001 00000 0
0000 11111 0
0000 00001 0
2. Implement in RISC V these line of code in C:
(i) f = g - A[B[C[27]]]
(ii) f = g - A[ C[10] + B[11] ]
(iii) A[i] = 4B[4i-44] + 3C[32i+32]
3. Hypersonic Computers, your employer, has just bought a new dual Core processor, and you
have been tasked with optimizing your software for this processor - for two applications on this
dual Core processor, but the resource requirements are not equal. The first one needs 80% of the
resources, and the second only 20%.
(i) Assume that 40% of the first application is parallelizable, how much speedup would
you achieve with that application if run in isolation?

Speed-up = 1/(0.6 + 0.4/2) = 1.25

Assume that 99% of the second application is parallelizable, how much speedup would this
application observe if run in isolation?

Speed-up = 1/(0.01 + 0.99/2) = 1.98

(iii) Given that 40% of the first application is parallelizable, how much overall system
speedup would you observe if you parallelized it? Given that 99% of the second application is
parallelizable, how much overall system speedup would you observe if you parallelized it?

Speed-up = 1/(0.2+0.8x0.6+0.8x[0.4/2]) = 1/(0.2+0.48+0.16)=1.19

Speed-up=1/(0.8+0.2x0.01+0.2x[0.99/2]) = 1/(0.8+0.002+0.099)=1.11

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SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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