In the following IEEE 754 representation, the decimal value of the stored number
ID: 3860313 • Letter: I
Question
In the following IEEE 754 representation, the decimal value of the stored number is 10111111100000000000000000000000 A.-1 b. -0 C. 0.1 D. -0.1 The 32-bit representation of a floating point number in the IEEE 754 standard is A. single precision b. in double precision c. as a scientific notation with right 8bits as a whole part and the left 24 bits as a fraction d. as a scientific notation with left 8bits as a whole part and the left 24 bits as a fraction In representing the decimal number 11/8 in IEEE 754 representation, the 8-bit binary value of the exponent plus bias for single precision is A. 01111111 B. 01111110 C. 01111101 D.10000000 In the following IEEE 754 representation, the value of the fraction of the number is 10111111100000000000000000000000 A. 0.1 in binary B. 0.1 in decimal C. 0 D. 0.75 Using sign bit in signed integer representation means that A. there is a binary code for 0 and a different binary code for -0 which is a wastage of a code B. the largest negative decimal number is greater in magnitude than the largest positive decimal number C. the sign bit also factors into determining the decimal value of the binary codes. After all, it is the most significant bit. D. a one followed by all zeros in a non-zero decimal number.Explanation / Answer
1) option A --> -1
Given IEEE 745 binary representation is 10111111100000000000000000000000 for this representation includes sign bit,exponent bits and mantissa.
* First bit represents sign bit here in our case first bit is "1" so it is a negative number.
* Now,exponent 8 bits are "01111111" --> 127 in decimal so,exponent is 2^0.
* Remaining 23 bits are mantissa bits all 23 bits are zeros so, mantissa value is 1.0.
2) Option A --> Single Precision
the 32 bit representation of floating point number in the IEEE 754 standard is single precision.Double precision is for 64 bit.
3) option A --> 01111111
In representing the decimal number 11/8 -> 1.375 and it is positive number for this sign bit is "0".
Fraction part -->
0.375*2 = 0.75
0.75*2 = 1.5
0.5*2 = 1.0
so, its representation is 1.011, here no need to move decimal point thus its exponent is "0". So, exponent bits value is 127+0 = 127. 127 in binary is 01111111.
Exponent 8 bits are "01111111" because of 2^0.
The mantissa bits are 01100000000000000000000.
4) option C --> 0
As stated in qestion 1 here the IEEE 754 binary reprasentation is 10111111100000000000000000000000.
so, as described number is -1.0 , Here its fractional part is "0".
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