Floating point rep is killing me.....please walk me through this. Thanks! 28 Con
ID: 3589594 • Letter: F
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Floating point rep is killing me.....please walk me through this. Thanks!
28 Consider the 64-bit double precision floating point number whose internal representation is shown below (in hexadecimal) 8010000000000000 Which of the following statements about that number is correct? A) The bit pattern represents infinity B) The bit pattern represents not-a-number. C) The bit pattern represents zero D) The bit pattern represents a denormal numbe:r E) The bit pattern represents a normalized number. 29. What is the decimal value of the 64-bit double precision floating point number whose internal representation is given below (in hexadecimal)? 4010800000000000 A) +0.125 B) +2.0625 C) +4.125 D) +8.25 E) None of the above 30 What is the 64-bit double precision internal representation in hexadecimal) of the decimal value given below? -6.75 (base 10) A) c02d800000000000 B) c01b000000000000 C) bfcd800000000000 D) bfdb000000000000 E) None of the aboveExplanation / Answer
1) Ans: is (E). The bit pattern represents a normalized number. Because the following decimal floating poit number can be represented in 64-bit binary floating point number as:
Bit 63 Bit 62 - 52 Bit 51 - 0
Sign-bit Exponent Field Significand
1 00000000001 1.0000000000000000000000000000000000000000000000000000
And the status of this binary number is normal, so it is valid.
For the same, if the conversion is 32-bit floating binary, then the status would have been underflow.
2) Ans: (C). The floating point binary representation of the above number is:
Bit 63 Bit 62 - 52 Bit 51 - 0
Sign-bit Exponent Field Significand
0 10000000001 1.0000100000000000000000000000000000000000000000000000
Decimal value of Decimal value of significand
exponent field and 1.0312500000000000
exponent: 1025 - 1023 = 2
Hence, the hexadecimal value is: 4.125.
3) ANS: (B)
The floating point binary representation of the above number is:
Bit 63 Bit 62 - 52 Bit 51 - 0
Sign-bit Exponent Field Significand
1 10000000001 1.10110000000000000000000000000000000000000000000000000
Decimal value of Decimal value of significand
exponent field and 1.6875000000000000
exponent: 1025 - 1023 = 2
Hence, the hex representtion of the above number is: C01B000000000000
THE LOGIC IS TO CONVERT EACH NUMBER IN FLOATING BINARY.
HOPE YOU GET IT, STILL IF ANY QUERIES, FEEL FREE TO ASK IN COMMENT SECTION.
THANK YOU.
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