Consider the following floating point number representation-
31 24 23 0
Exponent Maintissa
The exponent is in 2's complement representation and mantissa is in the sign magnitude representation in the range of. The magnitude of the normalised numbers in this representation is
Consider the following floating point number representation-
31 24 23 0
Exponent Maintissa
The exponent is in 2's complement representation and mantissa is in the sign magnitude representation in the range of. The magnitude of the normalised numbers in this representation is
The correct option is D 0.5 to (1−2−23)
The following floating point number
representation-
31 24
23 0
exponent mantissa
The exponent is in 2's complement representation
and mantissa is in the sign magnitude representation in the range of. The
magnitude of the normalized numbers in this representation is 0.5 to
(1-2−23).
Normalized numbers are of the form: 1.xxxx
xxxx… …xxxx {ignoring sign and exponent part}. They always have a Leading 1
before decimal point.
While storing such a number in this floating point representation two cases can
be there:
Case 1: We can store most significant 1 in
mantissa along with other bits as (while MSB of mantissa is a sign bit as ‘S’):
Minimum Mantissa=> S100 0000 0000 0000 0000 0000 = 1.00 0000…0000 = 1
Maximum Mantissa=> S111 1111 1111 1111 1111 1111 = 1.1111…1111 = 2 – 2-22.
Case 2: We can ignore to do so assuming an
implicit MSB as 1.
Minimum Mantissa=> S000 0000 0000 0000 0000 0000 = 1.000 0000…0000 = 1
Maximum Mantissa=> S111 1111 1111 1111 1111 1111 = 1.1111…1111 = 2 – 2-23.
The following floating point number
representation-
31 24
23 0
exponent mantissa
The exponent is in 2's complement representation
and mantissa is in the sign magnitude representation in the range of. The
magnitude of the normalized numbers in this representation is 0.5 to
(1-2−23).
Normalized numbers are of the form: 1.xxxx
xxxx… …xxxx {ignoring sign and exponent part}. They always have a Leading 1
before decimal point.
While storing such a number in this floating point representation two cases can
be there:
Case 1: We can store most significant 1 in
mantissa along with other bits as (while MSB of mantissa is a sign bit as ‘S’):
Minimum Mantissa=> S100 0000 0000 0000 0000 0000 = 1.00 0000…0000 = 1
Maximum Mantissa=> S111 1111 1111 1111 1111 1111 = 1.1111…1111 = 2 – 2-22.
Case 2: We can ignore to do so assuming an
implicit MSB as 1.
Minimum Mantissa=> S000 0000 0000 0000 0000 0000 = 1.000 0000…0000 = 1
Maximum Mantissa=> S111 1111 1111 1111 1111 1111 = 1.1111…1111 = 2 – 2-23.
