Question
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Express 1/16 in IEEE 32-bit floating-point format.

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Step 1

In the 32-bit IEEE format, the first bit is sign bit, the next 8 bits are assigned as the biased exponent, and the last twenty-three bits are the Fractional parts of the standardized number. If the number is a positive, the sign bit is 0, and if the number is negative, then sign bit is 1.

Convert the fractional value to decimal form-

(1/16) = 0.0625

Now, convert the decimal form to binary form-

Step 2

Add up together whole and fractional part here so:

(0)2 + (0.0001)2 = (0.0001)2

(0.0625)10 = (0.0001)2

It can also be represented as 1.0000 × (2)-4

For the Mantissa part-

Consider 23 bits after the decimal part in 1.0000 × (2)-4

So, here in this case all the 23 bits are zero.

Hence, the mantissa part for this is 00000000000000000000000

Step 3

Value of bias = 127+(-4)

= 123

Now for the exponent part, co...

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