Soalan 9:
Diberi 11223 + y7 = 1189, hitung nilai y.
Penyelesaian:
$$ \begin{aligned} 1122_3+y_7 & =118_9 \\ y_7 & =118_9-1122_3 \end{aligned} $$
$$ \begin{aligned} 118_9= & \left(1 \times 9^2\right)+\left(1 \times 9^1\right)+\left(8 \times 9^0\right) \\ & =81+9+8 \\ & =98_{10} \end{aligned} $$
$$ \begin{aligned} 1122_3 & =\left(1 \times 3^3\right)+\left(1 \times 3^2\right)+\left(2 \times 3^1\right)+\left(2 \times 3^0\right) \\ & =27+9+6+2 \\ & =44_{10} \end{aligned} $$
$$ 98_{10}-44_{10}=54_{10} $$
$$
54_{10}=105_7
$$
$$ \begin{aligned} 1122_3+y_7 & =118_9 \\ y_7 & =118_9-1122_3 \\ y_7 & =105_7 \\ y & =105 \end{aligned} $$
Diberi 11223 + y7 = 1189, hitung nilai y.
Penyelesaian:
$$ \begin{aligned} 1122_3+y_7 & =118_9 \\ y_7 & =118_9-1122_3 \end{aligned} $$
$$ \begin{aligned} 118_9= & \left(1 \times 9^2\right)+\left(1 \times 9^1\right)+\left(8 \times 9^0\right) \\ & =81+9+8 \\ & =98_{10} \end{aligned} $$
$$ \begin{aligned} 1122_3 & =\left(1 \times 3^3\right)+\left(1 \times 3^2\right)+\left(2 \times 3^1\right)+\left(2 \times 3^0\right) \\ & =27+9+6+2 \\ & =44_{10} \end{aligned} $$
$$ 98_{10}-44_{10}=54_{10} $$
$$
54_{10}=105_7
$$$$ \begin{aligned} 1122_3+y_7 & =118_9 \\ y_7 & =118_9-1122_3 \\ y_7 & =105_7 \\ y & =105 \end{aligned} $$
Soalan 10:
Isi tempat kosong dengan nombor urutan menaik mengikut asas yang diberikan.
Penyelesaian:
(a)
$$ \begin{aligned} 63_8 & =\left(6 \times 8^1\right)+\left(3 \times 8^0\right) \\ & =48+3 \\ & =51_{10} \end{aligned} $$
$$ \begin{aligned} 110100_2 & =\left(1 \times 2^5\right)+\left(1 \times 2^4\right)+\left(1 \times 2^2\right) \\ & =32+16+4 \\ & =52_{10} \end{aligned} $$
$$ \text { Maka, } 53_{10} \text { dalam asas } 8=65_8 $$
$$ 54_{10} \text { dalam asas } 2=110110_2 $$
(b)
$$ 124_{10} \text { dikekalkan dalam asas sepuluh } $$
$$ \begin{aligned} 148_9 & =\left(1 \times 9^2\right)+\left(4 \times 9^1\right)+\left(8 \times 9^0\right) \\ & =81+36+8 \\ & =125_{10} \end{aligned} $$
$$ \text { Maka, } 126_{10} \text { dalam asas } 8=176_8 $$
$$ 128_{10} \text { dalam asas } 5=1003_5 $$
Isi tempat kosong dengan nombor urutan menaik mengikut asas yang diberikan.
Penyelesaian:
(a)
$$ \begin{aligned} 63_8 & =\left(6 \times 8^1\right)+\left(3 \times 8^0\right) \\ & =48+3 \\ & =51_{10} \end{aligned} $$
$$ \begin{aligned} 110100_2 & =\left(1 \times 2^5\right)+\left(1 \times 2^4\right)+\left(1 \times 2^2\right) \\ & =32+16+4 \\ & =52_{10} \end{aligned} $$
$$ \text { Maka, } 53_{10} \text { dalam asas } 8=65_8 $$
$$ 54_{10} \text { dalam asas } 2=110110_2 $$
(b)
$$ 124_{10} \text { dikekalkan dalam asas sepuluh } $$
$$ \begin{aligned} 148_9 & =\left(1 \times 9^2\right)+\left(4 \times 9^1\right)+\left(8 \times 9^0\right) \\ & =81+36+8 \\ & =125_{10} \end{aligned} $$
$$ \text { Maka, } 126_{10} \text { dalam asas } 8=176_8 $$
$$ 128_{10} \text { dalam asas } 5=1003_5 $$