2.87 Floating-Point II

★

Problem:

Consider a 16-bit floating-point representation based on the IEEE floating-point format, with one sign bit, seven exponenet bits (k=7), and eight fraction bits (n=8). The exponent bias is 2^6-1=63.

Fill in the table that follows 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 signifcand field 0xC0 (binary 11000000), giving a hex representation 3EC0.

You need not fill in entries marked "--".

Desc	Hex	M	E	V	D
-0	0x8000	0	-14	-0	-0.0
Smallest value >2	0x4001	1025/1024	1	1025/512	2.001953125
512	0x6000	1	9	512	512.0
Largest denormalized	0x03FF	1023/1024	-14	1023/(1^24)	0.000060975551605
−∞	0xFC00	--	--	--	--
Number with hex representation 3BB0	--	123/64	-1	123/128	0.9609375