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Normalized Values - Computer Organization - Homework, Exercises of Computer Architecture and Organization

English and Foreign Languages UniversityComputer Architecture and Organization

These HOMEWOR NOTES are very easy to understand and very helpful to built a concept about the foundation of computers ORGANIZATION and Database Design.The key points in these slide are:Memory Hierarchy, Typical System View, Virtual Memory, Memory Management, Operating System, Degree of Multiprogramming, Resident R-Bit, Demand Paging, Page-Fault Trap, Physical Memory, Free Frame in Physical Memory

Typology: Exercises

2012/2013

Uploaded on 04/27/2013

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IEEE 754 Standard Floating Point Representation
Sign
32-bit
64-bit
128-bit
Sign
Sign
bit
bit
bit
Exponent
Exponent
Exponent
8-bit
11-bit
15-bit
23-bit Mantissa
52-bit Mantissa
112-bit Mantissa
(bias 127)
(bias 1023)
(bias 16,383)
(for normalized values, leading 1 not stored)
(for normalized values, leading 1 not stored)
(for normalized values, leading 1 stored)
0
0
0
1
1
1
+
+
+
-
-
-
Single Precision
Double Precision
Quad Precision
NaN (not a #)nonzero2,047nonzero255
infinity02,0470255
denormalized #nonzero0nonzero0
00000
normalized #any value1-2046any value1-254
RepresentedMantissaExponentMantissaExponent
ObjectDouble PrecisionSingle Precision
1) Convert the value 23.625
10
to its binary representation.
.
.5 .25 .125 .0625148163264 2
2) Normalize the above value so that the most significant 1 is immediately to the left of the radix point. Include the
corresponding exponent value to indicate the motion of the radix point.
1. x 2
3) Write the corresponding 32-bit IEEE 754 floating point representation for 23.625
10
.
4) Write the corresponding 128-bit IEEE 754 floating point representation for 23.625
10
.
Computer Organization Lecture 4 Name:________________
Lecture 4 Page 1
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Sign IEEE 754 Standard Floating Point Representation

32-bit 64-bit 128-bit

Sign Sign

bit bit bit

Exponent Exponent Exponent

8-bit 11-bit 15-bit

23-bit Mantissa 52-bit Mantissa 112-bit Mantissa

(bias 127) (bias 1023) (bias 16,383)

(for normalized values, leading 1 not stored) (for normalized values, leading 1 not stored) (for normalized values, leading 1 stored)

Single Precision Double Precision Quad Precision

2552550 nonzerononzero^0 2,0472,047^0 nonzerononzero^0 denormalized # NaN (not a #)infinity

Exponent 1-254 0 any value Mantissa 0 Exponent 1-2046 0 Mantissa any value 0 Represented normalized # 0 Single Precision Double Precision Object

  1. Convert the value 23.625 10 to its binary representation.

2) Normalize the above value so that the most significant 1 is immediately to the left of the radix point.^64 32168421^.^ .5^ .25^ .125^ .0625 Include the

corresponding exponent value to indicate the motion of the radix point. 1.

3) Write the corresponding 32-bit IEEE 754 floating point representation for 23.625x 2 10.

  1. Write the corresponding 128-bit IEEE 754 floating point representation for 23.625 10.

Computer Organization Lecture 4 Name:________________

Lecture 4 Page 1Docsity.com

  1. What would be the smallest positive normalized 32-bit IEEE 754 floating point value?

  2. How would you add two IEEE 754 floating point numbers?

  3. How would you multiply two IEEE 754 floating point numbers?

  4. Consider addinga) How many places does the second number's mantissa get shifted? 1.011 x 2^40 and 1.01 x 2^5. b) After we add these two numbers and store the results back into a 32-bit IEEE 754 value, what would be the result?

Computer Organization Lecture 4 Name:________________

Lecture 4 Page 2Docsity.com