Consider a 7-bit floating-point representation based on the IEEE floating-point
ID: 3865116 • Letter: C
Question
Consider a 7-bit floating-point representation based on the IEEE floating-point format, with one sign bit, three exponent bits (k = 3), and three fraction bits (n = 3). The exponent bias is 2311 = 3. The table that follows enumerates some of the values for this 7-bit floating-point representation. Fill in the blank table entries using the following directions:
e : The value represented by considering the exponent field to be an unsigned integer (as a decimal value)
E : The value of the exponent after biasing (as a decimal value)
2^E : The numeric weight of the exponent (as a decimal floating point value)
f : the value of the fraction (as a fractional decimal value such as 0.1234)
M : The value of the significand (as a floating value such as 1.2345) s*(2^E) * M : The value of the number in decimal (as a decimal floating point value). The 's' is equal to +1 if the number is positive and -1 if it is negative.
Do not use fractions and type the decimal values very precisely (accurate to the last decimal place).
1 010 010
0 011 111
1 000 101
Explanation / Answer
Bits
e
E
2^E
f
M
s*(2^E)*M
1 010 010
2
2-3=-1
2^-1
0.25
1.25
-1*(2^-1)* 1.25
0 011 111
3
3-3=0
2^0
0.875
1.875
+1*(2^0)* 1.875
1 000 101
0
0-3=-3
2^-3
0.625
1.625
-1*(2^-3)* 1.625
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If you have any query, please feel free to ask.
Thanks a lot.
Bits
e
E
2^E
f
M
s*(2^E)*M
1 010 010
2
2-3=-1
2^-1
0.25
1.25
-1*(2^-1)* 1.25
0 011 111
3
3-3=0
2^0
0.875
1.875
+1*(2^0)* 1.875
1 000 101
0
0-3=-3
2^-3
0.625
1.625
-1*(2^-3)* 1.625
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