GATE CS 2025 Set 2 — Question 49
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Digital Logic → Number Systems & Arithmetic → IEEE 754 Floating Point
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Question
Three floating point numbers , and are stored in three registers RX, RY, and RZ, respectively in IEEE 754 single precision format as given below in hexadecimal:Which of the following option(s) is/are CORRECT?
Correct answer
(A) 4(X + Y) + Z = 0; (B) 2Y - Z = 0; (C) 4X + 3Z = 0
Solution
We need to convert the IEEE 754 single precision hexadecimal representations to decimal values.The format is: 1 sign bit (), 8 exponent bits (), and 23 mantissa bits ().
The value is given by .1. Convert
Binary:
Binary:
Binary:
(A) . Correct.
(B) . Correct.
(C) . Correct.
(D) . Incorrect.Thus, options (A), (B), and (C) are correct.
The value is given by .1. Convert
Binary:
1100 0001 0001 0000 ... 0000- Sign (): 1 (Negative)
- Exponent ():
10000010= - Mantissa ():
0010000... - Value
Binary:
0100 0000 1100 0000 ... 0000- Sign (): 0 (Positive)
- Exponent ():
10000001= - Mantissa ():
1000000... - Value
Binary:
0100 0001 0100 0000 ... 0000- Sign (): 0 (Positive)
- Exponent ():
10000010= - Mantissa ():
1000000... - Value
(A) . Correct.
(B) . Correct.
(C) . Correct.
(D) . Incorrect.Thus, options (A), (B), and (C) are correct.
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