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計算機組織與結構
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Ch2 計算機算術（Arithmetic）
第 14 題／共 26 題
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CC 14/26
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14. Multiplier、Divider、Floating-Point Addition、ULP
#CC-02-014
難
Multiplier
Divider
Floating-Point Addition
ULP
📝
☆
Which of the following statements about computer arithmetic are correct?
A
(a) The hardware depicted in Fig. 5 above serves dual functions, functioning as both a multiplier and a divider. The Product/Remainder register necessitates a shift-right operation for multiplication and a shift-left operation for division. The control test unit receives its input from
P2
when operating as a multiplier and from
P1
when operating as a divider.
B
(b) For floating-point addition, aligning decimal points involves shifting the number with the smaller exponent to ensure proper alignment. This is because rounding the significand of the number with smaller exponent has a minor impact on accuracy. Conversely, if decimal points are aligned by shifting the number with the larger exponent, it may result in overflow on the significand of the number with the larger exponent.
C
(c) Addition is associative for both integers and floating-point numbers.
D
(d) Assuming the accuracy of a floating number is to the second decimal place and rounding half down with additional guard, round, and sticky bits. The ulp of the addition
5.01
×
10
2
+
1.56
×
10
5
5.01\times10^2 + 1.56\times10^5
5.01
×
1
0
2
+
1.56
×
1
0
5
is 0.499? (note: round_half_down(x) =
⌈
x
−
0.5
⌉
\lceil x-0.5\rceil
⌈
x
−
0.5
⌉
).
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