Consider a 9-bit floating-point representation based on the IEEE floating-point

Question

Consider a 9-bit floating-point representation based on the IEEE floating-point format, with one sign bit, four exponent bits (k = 4), and four fraction bits (n = 4). The exponent bias is 24-1-1-7. The table that follows enumerates some of the values for this 9-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) 2E: 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 2E M: The value of the number in decimal (as a signed decimal floating point value). The 's' is equal to +1 if the number is positive and -1 if it is negative. Finally, please DO NOT USE fractions and type the decimal values very precisely (accurate to the last decimal place). Bits e E 2 s*2E M 1110 1011 0 0110 1001 1 0000 1100

Explanation / Answer

1.

Bits: 1 1110 1011

e=11102 =1410

E=14-7=7

2E=27 =128

f=0.10112=0.5+0.125+0.0625=0.6875

M=1.6875

s*2E*M=(-1)*128*1.6875= -216 //sign bit negative

2.

Bits: 0 0110 1001

e=01102 =610

E=6-7= -1

2E=2-1 =0.5

f=0.10012=0.5+0.0625=0.5625

M=1.5625

s*2E*M=(+1)*0.5*1.5625= 0.78125 //sign bit positive

3.

Bits: 1 0000 1100

e=00002 =010

E=0-7= -7

2E=2-7 =0.0078125

f=0.11002=0.5+0.25=0.75

M=1.75

s*2E*M=(-1)*0.0078125*1.75= -0.013671875 //sign bit negative

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