number system-addition and subtaction

用戶100934

2007-01-11 1:46 am

我想問直式點計到出黎

1 1010(2)+1110(2)

1010
+1110
-------------
11000

DE
+AB
----------
189

E(16)+B(16)=19(16) 點樣得出呢個結果?

減數點計?

回答 (1)

2007-01-11 8:44 am

✔ 最佳答案

In base-10,
123
= (10)^2 * 1 + (10)^1 * 2 + (10)^0 * 3
= 100 + 20 + 3
= 123

In base-16,
DE
= (16)^1 * 13 + (16)^0 * 14
= 208 + 14
= 222

Similarly, convert base-16 to base-10:
E = 14
B = 11
E + B = 25

25 / 16 = 1 with remainder 9
thus = 19 (base-16)

Subtraction:
Same idea...

For example:
DE - F

E is smaller than F, so you borrow 1 (i.e. 16 because it is base-16) from the left digit D, D - 1 becomes C.
Add the 1 to the right digit:
(E + 16) - F
= 30 - F
= 30 - 15
= 15

Attaching left digit C to 15, we have CF

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