7. Consider a floating point representation with a sign bit, a 5 bit exponent an
ID: 3600204 • Letter: 7
Question
7. Consider a floating point representation with a sign bit, a 5 bit exponent and a 10 bit significand. Assume the exponent uses excess M representation uses an implied 1 leading bit a. What is the largest integer that can be represented in this format? b. What is the smallest positive integer that can be represented? c. How many base 10 digits are accurately represented? d. What number is represented by 0010100010111010? with an offset of 15. Assume the significand sider a set of valid codes from a much large set of possible codes. The distance between two codes is the number of bits in which the two codes differ, and the Hamming distance is the minimal distance between any two valid codes. Why is this far more useful than the average distance between any two valid codes? The following is a Hamming code: 01111010110001101010. Does it contain an error? If so, and assuming an error in only I bit, what is the correct code? 9. broken into a number of small chunks, each of which is encoded separately. There is a trade-off between using long chunks and short chunks. What is the primary advantage of using longer chunks? What is the advantage of using short chunks? What is the one key factor that would be used to decide the size chunk to use? 10. When using Hamming codes to encode a very long binary message, typically the message isExplanation / Answer
Answer 7 )
a) largest integer = 1.1111111111 x 2^(31-15)
it's written implied 1 in question , so before dot put a 1. Then u have 10bits as significand or mantissa .So when will it be maximum? when all 1 would be there in all the 10bits. so 1.1111111111 . Then the exponent part has 5 bits.When it will be maximum .When all ones are there...11111 = 31 ....but excess 15 is used.so u need to subtract it from 31...31-15 = 16 . Now ans is simple...1.1111111111 x 2^16.
b) Similarly smallest positive number can be represented as nopes = 1.0000000000 x 2^(-15) .
(c) We have 1 sign bit and 10 bit mantissa or significand So total 11 bits .In binary number system we can represent 2^11 numbers with it. Now in decimal number system base is 10. So lets see how many bits can be suggessfully represented..just equate 2^11=10^x, take log and solve for x .
11(log<base10> 2 ) = x log<base 10> 10
x=11 log<base10> 2
x=3
d) The binary number in question is 0010100010111010, it represents 1.0010111010 x 2^(10-15) . 1st bit is sign bit , next 5 bits are exponent bits , next 10bits are mantissa bits.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.