Question

# Consider a 16-bit floating-point representation based on the IEEE floating-point format, with one sign bit, seven

exponent bits (k = 7), and eight fraction bits (n = 8). The exponent bias is 2^(7−1) − 1 = 63.

Fill in the table (shown in Figure 1) for each of the numbers given, with the following instructions for each column.

Hex: The four hexadecimal digits describing the encoded form.

M: The value of the significand. This should be a number of the form x or x/y , where x is an integer, and y is an integral power of 2. Examples include: 0, 67/64 , and 1/256

E: The integer value of the exponent.

V : The numeric value represented. Use the notation x or x × 2^z, where x and z are integers.

As an example, to represent the number 7/8 , we would have s = 0, M = 7 4 , and E = −1. Our number would therefore have an exponent field of 0x3E (decimal value 63 − 1 = 62) and a significand field 0xC0 (binary 11000000), giving a hex representation of 3EC0.

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