# A) Calculate (3 984375 x 10^ 1 + 3 4375 x 10^ 1) + 1 771 x 10^3by

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a) Calculate (3.984375 x 10^-1 + 3.4375 x 10^-1) + 1.771 x
10^3
by hand, assuming each of the values are stored in the 16-
bit half precision format
described in Exercise 3.27 (and also described in the text).
Assume 1 guard, 1
round bit, and 1 sticky bit, and round to the nearest even.
Show all the steps, and
and in decimal.
b.) Calculate 3.984375 x 10^-1 + (3.4375 x 10^-1 + 1.771 x
10^3)
by hand, assuming each of the values are stored in the 16-
bit half precision format
described in Exercise 3.27 (and also described in the text).
Assume 1 guard, 1
round bit, and 1 sticky bit, and round to the nearest even.
Show all the steps, and
and in decimal.
Solution
a)(3.984375 * 10-1 + 3.4375 * 10-1) + 1.771 *103
3.984375 * 10-1 = 1.1001100000 * 2-2
3.4375 * 10-1 = 1.0110000000 * 2-2
1.771 * 103 = 1.1011101011 * 210
Therefore 3.984375 * 10-1 + 3.4375 * 10-1 =

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1.1001100000 * 2-2 +
1.0110000000 * 2-2
10.1111100000 * 2-2 =>Normalize to form
1.01111100000 * 2-1
i.e. (3.984375 * 10-1 + 3.4375 * 10-1) + 1.771 *103 =
1.01111100000 * 2-1 + 1.1011101011 * 210 =
1.01111100000 * 2-1= .0000000000 10
1111100000 * 210 ;Guard =1;Round=0; Sticky=1
Therefore (3.984375 * 10-1 + 3.4375 * 10-1) + 1.771
*103 =
0.0000000000 10 1111100000 *210 +
1.1011101011 * 210= 1.101110101110 1111100000 *210 ;
Round up to
form = 1.
1011101100 * 210
= 0000011011101100
= 1772
b) 3.984375 * 10-1 + (3.4375 * 10-1 + 1.771 *103)
3.984375 * 10-1 = 1.1001100000 * 2-2 = .0000000000
011001100000 * 210
3.4375 * 10-1 = 1.0110000000 * 2-2 = .0000000000 01
0110000000 * 210; Guard = 0; Round =1; Sticky =1
1.771 * 103 = 1.1011101011 * 210
Therefore, 3.4375 * 10-1+1.771 * 103 = .0000000000 *
210 + 1.1011101011 * 210

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a) Calculate (3.984375 x 10^-1 + 3.4375 x 10^-1) + 1.771 x 10^3 by hand, assuming each of the values are stored in the 16 bit half precision format described in Exercise 3.27 (and also described in the text). Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps, and write your answer in both the 16 -bit fl oating point format and in decimal. b.) Calculate 3.984375 x 10^-1 + (3.4375 x 10^-1 + 1.771 x 10^3) by hand, assuming each of the values are stored in the 16bit half precision format described in Exercise 3.27 (and also described in the text). Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps, and write your answer in both the 16 -bit fl oating point format and in decimal. Solution a)(3.984375 * 10-1 + 3.4375 * 10-1) + 1.771 *103 3.984375 * 10-1 = 1.1001100000 * 2-2 3.4375 * 10-1 = 1.011000000 ...
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