Number-Systems
November 12, 2024Number-Systems
November 12, 2024Number-Systems
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Question 25
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The following is a scheme for floating point number representation using 16 bits.
Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is:
What is the maximum difference between two successive real numbers representable in this system?
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2-40
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2-9
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222
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231
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Question 25 Explanation:
Largest gap will be in between two most largest numbers.
The largest number is 1.111111111× 262-31 = (2−2−9)×231
Second largest number is 1.111111110×262-31 = (2−2-8)×231
Difference = (2−2−9)×231 – (2−2-8)×231
= (2-8−2−9) ×231
= 2−9×231
= 222
The largest number is 1.111111111× 262-31 = (2−2−9)×231
Second largest number is 1.111111110×262-31 = (2−2-8)×231
Difference = (2−2−9)×231 – (2−2-8)×231
= (2-8−2−9) ×231
= 2−9×231
= 222
Correct Answer: C
Question 25 Explanation:
Largest gap will be in between two most largest numbers.
The largest number is 1.111111111× 262-31 = (2−2−9)×231
Second largest number is 1.111111110×262-31 = (2−2-8)×231
Difference = (2−2−9)×231 – (2−2-8)×231
= (2-8−2−9) ×231
= 2−9×231
= 222
The largest number is 1.111111111× 262-31 = (2−2−9)×231
Second largest number is 1.111111110×262-31 = (2−2-8)×231
Difference = (2−2−9)×231 – (2−2-8)×231
= (2-8−2−9) ×231
= 2−9×231
= 222