1. 62∨(10)=
2. Represent each of the following by a binary number.
1×2^4+0×2^3+1×2^2+0×2^1+1
3. Write down the following numbers in expanded form.
11110∨(2)
4. Simplify the following expressions.
(a) (x^3/y^2)^4.(x^2y)^3
(b) a^2×a^3×b^4/(a^2b^3)
(c) (-4a)^3/(-2ab)^2
5. Convert 110110∨(2) into a denary number.
6. Convert 37∨ (10) into a binary number.
7. Convert 444∨(10) into a hexadecimal number.
8. Convert the following binary numbers into hexadecimal numbers.
111101110101∨2
9. Convert the following hexadecimal numbers into binary numbers.
9C∨16
10. There are mistakes in the shaded parts. Make necessary
corrections.
(a) 2^3×3^2=(2×3)^3+2=6^5(the shaded part is =(2×3)^3+2=6^5)
(b) (-a^2)^3=a^2×3=a^6(the shaded part is =a^2×3=a^6)
(c) (a^2)^3=a^5(the shaded part is =a^5)
(d) a^10.a^2/a^5.a^6=a^10+2-5+6=a^13(the shaded part is=a^10+2-5+6=a^13 )
數條中一英文數學題(未必答曬)
2009-08-11 2:13 am
回答 (2)
2009-08-11 3:33 am
✔ 最佳答案
1. 62(10)
= 6x10 + 2 ...... (ans)
2.
The binary number = 10101 ...... (ans)
3.
Expanded form
= 1x2^4 + 1x2^3 + 1x2^2 + 1x2^1 + 0 ...... (ans)
4.
(a) (x^3/y^2)^4.(x^2y)^3
= (x^12/y^8).(x^6y^3)
= x^(12+6).y^(-8+3)
= x^18.y^(-5)
= x^18/y^5 ...... (ans)
(b) a^2×a^3×b^4/(a^2b^3)
= a^(2+3+2).b^(4-3)
= a^7b ...... (ans)
(c) (-4a)^3/(-2ab)^2
= (-4)^3a^3/(-2)^2a^2b^2
= -64a^3/4a^2b^2
= (-64/4)a^(3-2)/b^2
= -16a/b^2 ...... (ans)
5.
110110(2)
= 1x2^5 + 1x2^4 + 0x2^3 + 1x2^2 + 1x2^1 + 0
= 32 + 16 + 0 + 4 + 2 + 0
= 54(10) ...... (ans)
6.
37/2 = 18 ... 1
18/2 = 9 ... 0
9/2 = 4 ... 1
4/2 = 2 ... 0
2/2 = 1 ... 0
27(10) = 100101(2) ...... (ans)
7.
444/16 = 27 ... 12=C
27/16 = 1 ... 11=B
444(10) = 1BC(16) ...... (ans)
8.
111101110101(2)
= 1111(2)x2^8 + 111(2)x2^4 + 101(2)
= (2^3 + 2^2 + 2^1 + 1)x16^2 + (2^2 + 2^1 + 1)x16 + (2^2 + 1)
= (8 + 4 + 2 + 1)x16^2 + (4 + 2 + 1)x16 + (4 + 1)
= 15x16^2 + 7x16 + 5
= F75(16) ...... (ans)
9.
9/2 = 4 ... 1
4/2 = 2 ... 0
2/1 = 1 ... 0
12/2 = 6 ... 0
6/2 = 3 ... 0
3/2 = 1 ... 1
9C(16)
= 9x16 + 12
= 1001(2)x2^4 + 1100(2)
= 10011100(2) ...... (ans)
10.
(a)
Correction:
2^3 x 3^2 cannot be simplified by using index laws. ...... (ans)
(b)
Correct:
(-a^2)^3 = [(-1).a^2]^3 = (-1)^3.a^(2x3) = -a^6 ...... (ans)
(c)
Correction:
(a^2)^3 = a^(2x3) = a^6 ...... (ans)
(d)
Correction:
a^10.a^2/a^5.a^6 = a^(10+2-5-6) = a ...... (ans)
2009-08-11 2:40 am
1. 62(10) is a denary number , so the answer is 62 naturally .
2.1×2^4+0×2^3+1×2^2+0×2^1+1 = 10101(2) .
3.1×2^4+1×2^3+1×2^2+1×2^1+0 ( expanded form )
5.110110(2) is a binary number , so the answer is
1*2^5+1*2^4+0*2^3+1*2^2+1*2^1+0 = 54(10)
6. 37(10) is a denary number , so the answer is 100101(2) .
7. 444(10) is a denary number , so the answer is 1BC(16) .
8.111101110101(2) is a binary number , so the answer is
1*2^11+1*2^10+1*2^9+1*2^8+0*2^7+1*2^6+1*2^5+1*2^4+0*2^3+1*2^2+0*2^1+1 = 3957(10) .
3957(10) = F75(16)
9.9C(16) is a hexadecimal numbers , so the answer is 10011100(2)
第4and10條未能幫你解答 . 好對不起 .
2.1×2^4+0×2^3+1×2^2+0×2^1+1 = 10101(2) .
3.1×2^4+1×2^3+1×2^2+1×2^1+0 ( expanded form )
5.110110(2) is a binary number , so the answer is
1*2^5+1*2^4+0*2^3+1*2^2+1*2^1+0 = 54(10)
6. 37(10) is a denary number , so the answer is 100101(2) .
7. 444(10) is a denary number , so the answer is 1BC(16) .
8.111101110101(2) is a binary number , so the answer is
1*2^11+1*2^10+1*2^9+1*2^8+0*2^7+1*2^6+1*2^5+1*2^4+0*2^3+1*2^2+0*2^1+1 = 3957(10) .
3957(10) = F75(16)
9.9C(16) is a hexadecimal numbers , so the answer is 10011100(2)
第4and10條未能幫你解答 . 好對不起 .
參考: Calculator and myself
收錄日期: 2021-04-13 16:47:22
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