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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.
Which one of the following is FALSE?
Which one of the following is FALSE?
- a)A + C = 0
- b)C = A + B
- c)B = 3C
- d)(B - C) > 0
Correct answer is option 'B'. Can you explain this answer?
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Consider three floating-point numbers A, B and C stored in registers R...
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:
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.
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:
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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Consider three floating-point numbers A, B and C stored in registers RA, RBand 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.Which one of the following is FALSE?a)A + C = 0b)C = A + Bc)B = 3Cd)(B - C) > 0Correct answer is option 'B'. Can you explain this answer?
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