Consider three floating-point numbers A, B and C stored in registers RA, RB and RC, respectively as per IEEE-754 single-precision floating point format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.

RA= 0xC1400000  RB = 0x42100000 RC = 0x41400000  


Which one of the following is FALSE?

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  1. A + C = 0
  2. C = A + B
  3. B = 3C
  4. (B - C) > 0

Answer (Detailed Solution Below)

Option 2 : C = A + B
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The correct answer is option 2.

Concept:

IEEE single-precision floating-point:

IEEE single-precision floating-point computer numbering format is a binary computing format that takes up 4 bytes (32 bits) of memory. Binary32 is the official name for the 32-bit base 2 formats in IEEE 754-2008. IEEE 754-1985 referred to it as single.

IEEE single-precision format:

F1 Madhuri Engineering 28.03.2022 D36

Explanation:

The given data,

Decimal value =(-1)s x 1.M x 2Base Exponent -Bias

Bias value in IEEE single-precision format is 127

RA = 1100 0001 0100 0000 0000 0000 0000 0000

RA sign= 1

RA Base Exponent =100 0001 0 = 130

RA Mantisa = 100 0000 0000 0000 0000 0000 = 1.100 0000 0000.....

Decimal value = (-1)1 x1.1 x2130-127 =-1.1x23= -1100 = (-12)10

A=-12

RB = 0100 0010 0001 0000 0000 0000 0000 0000

RA sign= 0

RA Base Exponent =100 0010 0= 132

RA Mantisa = 001 0000 0000 0000 0000 0000 = 1.001 000000.....

Decimal value = (-1)0 x1.001 x2132-127 =+1.001x25= + 100100 = (+36)10

B=+36

RC = 0100 0001 0100 0000 0000 0000 0000 0000

RA sign= 0

RA Base Exponent =100 0001 0= 130

RA Mantisa =100 0000 0000 0000 0000 0000= 1.100 0000.....

Decimal value = (-1)0 x1.1 x2130-127 =+1.1x23= + 1100 = (+12)10

C=+12

Option 1: A + C = 0

True, A+C= -12+12=0

Hence it is true.

Option 2: C = A + B

False, A+B= -12+36=+24

it not equal to C. Hence it is false.

Option 3: B = 3C

True, B=3C 

=3x+12 =36 =B

it equal to B. Hence it is true.

Option 4: (B - C) > 0

True, (B-C) >0

=(36-12)=24>0

Hence it is true.

Hence the correct answer is C = A + B.

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