唔識進數..教一教我

1.把下列數字以展開式表示:
a. 11110(2)

=1x2^4 1x2^3 1x2^2 1x2^1 0x2^0

b. 4AB(16)

=4x16^2 Ax16^1 Bx16^0

2.把2E1(16) 轉換十進數

2E1(16)

=2x16^2 14x16^1 1x16^0
=2x256 14x16 1
=737(10)

3.把110110(2)轉換為進數

=1x2^5 1x2^4 0x2^3 1x2^2 1x2^1 0x2^0
=1x32 1x16 0x8 1x4 1x2 0x2^0
=54(10)

4.把37(10)轉換為二進數

用短除法:

2 ) 37 ----> 餘1
2 ) 18 ----> 餘0
2 ) 9 ----> 餘1
2 ) 4 ----> 餘0
2 ) 2 ----> 餘0
1

答案: 由尾數番上頭
=100101

5.把444(10)轉換為十六進數

先用用短除法, 轉為二進數:

2 ) 444 ----> 餘0
2 ) 222 ----> 餘0
2 ) 111 ----> 餘1
2 ) 55 ----> 餘1
2 ) 27 ----> 餘1
2 ) 13 ----> 餘1
2 ) 6 ----> 餘0
2 ) 3 ----> 餘1
1

由尾數番上頭
=110111100

再轉為十六進數
以四個二進數鴒為一組,
0001 1011 1100
先看第一組
0001(2) =1(10) =01(16)
再看第二組
1011(2) =11(10) =0B(16)
再看第三組
1100(2) =12(10) =0C(16)

答案:
010B0C(16)

仲有..順便可以教教我點計 十進數...二進數...十六進數...OK可以嗎?

十進數--->二進數
如上, 先用用短除法, 轉為二進數
然後, 由下而上, 將餘數連起即可

二進數--->十六進數
如上, 以四個二進數為一組,
如果最左面唔夠四個二進數, 就加 多幾個0

然後, 逐一組化為十六進數:
1010(10) = A(16)
1011(10) = B(16)
1100(10) = C(16)
1101(10) = D(16)
1110(10) = E(16)
1111(10) = F(16)

二進數--->十進數

將二進數展開成次方, 例如
=1x2^4 1x2^3 1x2^2 1x2^1 0x2^0
由右至左, 從2的 0, 1, 2 ,3 次方列出
然後對應每個位的數值, 算出答案

十六進數--->十進數

將十六進數展開成次方, 例如
2E1(16)
=2x16^2 14x16^1 1x16^0
由右至左, 從16的 0, 1, 2 ,3 次方列出
然後對應每個位的數值, 算出答案


6.把下列二進數轉換為十六進數{每四個位的二進數可直接轉換為一個位的十六進數}

a. 111101110101(2)

1111 0111 0101(2)

=0F75(16)


7. 把下列十六進數轉換為二進數{每一個位的十六進數可直接轉換為四個位的二進數}

a. 9C (16)
9 (16) =1001(2)
C (16) =1010(2)

答案:
=1001 1010(2)

b. 24D(16)

2 (16) = 0010(2)
4 (16) = 0100(2)
D (16) =1101(2)

答案:
= 0010 0100 1101(2)

下列{ } 中出了錯..把錯處改正

1. 2的3次方 x 3的2次方 錯---> { = (2 x 3)3次方 2 = 6的5次方 }

= 2^3 x 3^2

2. (-a 2次方)3次方 錯--->{ = a 2次方x3次方 = a 2x3的次方 = a 6的次方 }

= (-a^2)^3
= -a^6

3. (a的2次方)3次方 錯--->{ = a的5次方 }

= (a^2)^3
= a^6


4. a5次方．a6次方 分之 a10次方． a2 次方 錯--->{ = a 10 2-5 6次方 = a的13次方 }

= (a^10．a^2)/(a^5．a^6)
= (a^12)/(a^11)
= a

1.把下列數字以展開式表示:
a. 11110(2) b. 4AB(16)

1a) 1x2^4 + 1x2^3 + 1x2^2 + 1x2^1 + 0x2^0 = 16+8+4+2+0 =30
1b) 4x16^2 + Ax16^1 +Bx16^0 where A = 10, B=11 sub the number back you should have ur ans.
u know in 16's A = 10, B =11, C=12,.., all the way to F =15

2.把2E1(16) 轉換十進數
same as #1
2E1 = 2x16^2 + Ex16^1 +1x16^0 where E = 14

3.把110110(2)轉換為進數
same as #1
1x2^5 + 1x2^4 + 0x2^3 + 1x2^2 + 1x2^1 + 0x2^0

4.把37(10)轉換為二進數
take the remainders everytime u divide 2
37/2 = 18 r=1
18/2 = 9 r =0
9/2 = 4 r = 1
4/2 = 2 r = 0
2/2 = 1 r =0
1/2 r=1

look @ the r's, 37(10) = 100101(2) read from bottom to top

5.把444(10)轉換為十六進數 same as 2
take the remainders everytime u divide 16
444 mod 16 = 12 =C (and 444/16 =17 r =12) (mod is a dividing method which look for remainder only)
27 mod 16 = 11 = B
1 mod 16 =1

444(10) = 1BC(16) read from bottom to top

U can use ur calcalor in ur computer to check to
change that to scientific mode
it will has Hex(16) , Oct(8) , Dec(10), Bin(2)

I will answer the rest later
hope that helps~