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Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.
If R3 = R1/R2, what is the value stored in R3?
  • a)
    0x40800000
  • b)
    0xC0800000
  • c)
    0x83400000
  • d)
    0xC85800000
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Consider three registers R1, R2 and R3 that store numbers in IEEE-754 ...
In IEEE- 754 single precision format, a floating-point number is represented in 32 bits.

Sign bit value 0 means positive number, and 1 means a negative number.

The floating-point number can be obtained by formula: ± 1. M × 2(E-127)

Data:

Content of R1: 0x 42200000               (0x means Hexadecimal notation)

Content of R2: 0x C1200000

Calculation:
Content of R1 in Hex (0x) is 42200000. After converting into binary, it can be represented in IEEE- 754 format as:


Sign bit is 0 i.e. the number is positive

Biased Exponent (E’) = 100 0010 0 = 132

Normalized Mantissa (M) = 010 0000 0000 0000 0000 0000 = .25

Therefore, the number in register R1 = + 1.25 * 2(132-127) = 1.25 × 32 = 40
Content of R2 in Hex (0x) is C1200000. After converting into binary, it can be represented in IEEE- 754 format as:


Sign bit is 1 i.e. the number is negative

Biased Exponent (E’) = 100 0001 0 = 130

Normalized Mantissa (M) = 010 0000 0000 0000 0000 0000 = .25

Therefore, the number in register R1 = - 1.25 * 2(130-127) = -1.25 * 8 = -10

R3 = R1/R2 = 40/-10 = -4

Since the number is negative, Sign bit (MSB) = 1

Converting 4 into binary of a floating point gives: (100.0)2

Representing it into normalized form gives:  (1.000000….) × 22

Therefore, Mantissa is 23 bits of all 0s

Biased Exponent (E’) = E+ 127 = 2+127 = 129 = (10000001)2
It can be represented in IEEE- 754 format as:


Converting it into Hex format gives: 0x C0800000
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Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.If R3 = R1/R2,what is the value stored in R3?a)0x40800000b)0xC0800000c)0x83400000d)0xC85800000Correct answer is option 'B'. Can you explain this answer?
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