f4.maths 40MARKS

Maths Error~
Decimal no. : 2009= 2*10^3+0*10^2+0*10^1+9*10^0
So on the Binary no.expressed in the expanded form with base 2,
But 2009 cannot be calculated

2007-07-21 21:35:43 補充：
Found it during using calculator

1. Subtract the maximum number of power of two (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048……) which can be subtracted from the decimal number.

2. Mark the bit which corresponds to the number of power of two which could be subtracted as "1", otherwise mark the bit as “0”.

3. Repeat Step 1 on the remainder until the remainder passes away.


4. Hereinafter, repeat similar subtraction The row of "1" and "0" by above result is a binary number.


eg. "2009"
2009 - 1024 = 985
985 – 512 = 473
473 - 256 = 217
217 - 128 = 89
89 - 64 = 25
25 - 16 = 9
9 - 8 = 1

bit 1024 512 256 128 64 32 16 8 4 2 1
binary 1 1 1 1 1 0 1 1 0 0 1

The answer is 11111011001.

11111011001

用電腦的小算盤就可以輕易轉換
在檢視--->工程型

2007-07-21 21:27:04 補充：
數學計法就將佢係咁除２2009 / 2 = 1004 ... 11004 / 2 = 502 ... 0502 / 2 = 251 ... 0251 / 2 = 125 ... 1125 / 2 = 62 ... 162 / 2 = 31 ... 031 / 2 = 15 ... 115 / 2 = 7 ... 17 / 2 = 3 ... 13 / 2 = 1 ... 1116(10) = 10000(2) 將十進制的數不斷除二，抽餘數，直至商數為1為止才停止。二進制的數是由下(1)而上讀上來。

2007-07-23 01:13:31 補充：
16(10) = 10000(2)