GATE CS 2026 Set 1 — Question 36
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Digital Logic → Number Systems & Arithmetic → IEEE 754 Floating Point
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Question
Consider the real valued variables and represented using the IEEE 754 single-precision floating-point format. The binary representations of and in hexadecimal notation are as follows:Let .Which one of the following is the binary representation of , in hexadecimal notation?
Correct answer
(C) 35E80000
Solution
To find the value of , we first decode the IEEE 754 single-precision representations of and .1. Decode (35C00000):
- Hexadecimal:
3 5 C 0 0 0 0 0 - Binary:
0011 0101 1100 0000 ... - Sign bit (): (Positive)
- Exponent ():
01101011 - Decimal value:
- Actual exponent ():
- Mantissa ():
1000... - Significand:
- Value of :
- Hexadecimal:
3 4 A 0 0 0 0 0 - Binary:
0011 0100 1010 0000 ... - Sign bit (): (Positive)
- Exponent ():
01101001 - Decimal value:
- Actual exponent ():
- Mantissa ():
0100... - Significand:
- Value of :
- Align the exponents to the larger one ().
- (Shift right by 2 positions)
- Add the significands:
- Result:
- Sign:
- Exponent: Same as (), so biased exponent is (
01101011). - Mantissa:
1101000...(drop the leading 1) - Construct the 32-bit string:
- Sign:
0 - Exponent:
01101011 - Mantissa:
11010000000000000000000 - Combined:
0011 0101 1110 1000 0000 ...
00113010151110E10008- Remaining zeros 0000
- Result: 35E80000
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