多項數學題

以展式表示:
(a)
1001(2)
= 1*10³ + 1

(b)
F99D
= 15*16³ + 9*16² + 9*16 + 13


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把以下兩個二進數化為十進數:
(a)
10(2)
= 1*2
= 2(10)

(b)
110(2)
= 1*2² + 1*2
= 6(10)


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把以下兩個十進數化為二進數:
(a)
2 | 9
2 | 4 ...... 1
2 | 2 ...... 0
__­ 1 ...... 0

所以 9(10) = 1001(2)

(b)
2 |­35
2 |­17 ...... 1
2 | 8 ...... 1
2 | 4 ...... 0
2 | 2 ...... 0
__ 1 ...... 0

所以35(10) = 100011(2)


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把以下兩個十六進數化為十進數:
(a)
4E6B(16)
= 4*16³ + 14*16² + 6*16 + 11
= 20075(10)

(b)
4C59(16)
= 4*16³ + 13*16² + 5*16 + 9
= 19801(10)


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以小數表示以下兩個數:
(a)
5 * 10⁻²
= 5 * 0.01
= 0.05

(b)
7.5 * 10⁻³
= 7.5 * 0.001
= 0.0075


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以科學記數法表示以下兩個數:
(a)
8000
= 8 * 1000
= 8 * 10³

(b)
0.074
= 7.4 * 0.01
= 7.4 * 10⁻²


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把以下兩條數式寫成十進數:
(a)
4*10² + 8*10 + 1
= 481

(b)
5*10⁴ + 2*10³ + 3*10 + 1
= 52031


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把以下兩條數式寫成二進數:
(a)
1*2² + 1*2 + 1*1
= 111

(b)
1*2³ + 0*2² + 1*2 + 0*1
= 1010


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把以下兩條數式寫成十六進數:
(a)
3*16² + 10*16¹ +11
= 3AB

(b)
8*16³ + 0*16² + 1*16¹ + 15
= 801F


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解以下兩條方程:
(a)
10^x = 0.01
10^x = 10^-2
x = -2

(b)
3^(2x) = 1/27^4
3^(2x) = (3^-3)^4
3^(2x) = 3^(-12)
2x = -12
x = -6

(c)
2^(x+2) - 2^x = 48
(2^2)*2^x - 2^x = 48
4*2^x - 2^x = 48
3*2^x = 48
2^x = 16
2^x = 2^4
x = 4