數系題（中一升中二）

(1)
把下列數字以展開式表示：

1.
111102
= 1x24 + 1x23 + 1x22 + 1x21 + 0

2.
4AB16
= 4x162 + 10x161 + 11


(2)
把2E116轉換為十進數。
2E116
= 2x162 + 14x161 + 1
= 73710

把1101102轉換為十進數。
1101102
= 1x25 + 1x24 + 0x23 + 1x22 + 1x21 + 0
= 5410

把 3710 轉換為二進數。
37/2 = 18 ... 1
18/2 = 9 ... 0
9/2 = 4 ... 1
4/2 = 2 ... 0
2/2 = 1 ... 0
所以 3710 = 1001012

把 44410 轉換為十六進數。
444/16 = 27 ... 12 = C
27/16 = 1 ... 11 = B
所以 44410 = 1BC16


(3)
把下列二進數轉換為十六進數。（提示：每四個位的二進數可直接轉換為一個位的十六進數。）

1.
10110112
= 1012x100002 + 10112
= (1x22 + 0x21 + 1)x24 + (1x23 + 0x22 + 1x21 + 1)
= 5x16 + 11
= 5B16

2.
1111011101012
= 11112x1000000002 + 111x100002 + 1012
= (100002 - 12)x28 + (10002 - 12)x24 + (1002 + 1)
= (24 - 1)x162 + (23 - 1)x161 + (4 + 1)
= 15x162 + 7x161 + 5
= F7516

* = 乘
^ = 次方

第一題係轉成十進數??
(1) 1. 30
2. 1195

(2) 1. 737
2. 54
3.100101
4. 1BC

(3) 1. 5B
2. F75

1. 11110(2)
=1*2^5+1*2^4+1*2^3+1*2^2

4AB(16) = 4*16^3+10*16^2+11*16^1

2.
2E1(16) =2*16^3+14*16^2+1 =8192+3574+1 =11767

110110(2)=1*2^6+1*2^5+1*2^3+1^2^2 =62+32+8+4 =108

37= 100101

444=1BC


3.

1011011 =5B
since 101= 5,1011= B


111101110101= F 7 5
since 1111 = F
0111=7
0101 =5