Soalan 8:
Hitung hasil tambah nilai digit 8 dan nilai digit 3 dalam nombor 18239.
Penyelesaian:
$$ 1823_9=\left(1 \times 9^3\right)+\left(8 \times 9^2\right)+\left(2 \times 9^1\right)+\left(3 \times 9^0\right) $$
$$ \begin{aligned} &\text { Hasil tambah nilai digit } 8 \text { dan nilai digit } 3\\ &\begin{aligned} & =\left(8 \times 9^2\right)+\left(3 \times 9^0\right) \\ & =648+3 \\ & =651 \end{aligned} \end{aligned} $$
Hitung hasil tambah nilai digit 8 dan nilai digit 3 dalam nombor 18239.
Penyelesaian:
$$ 1823_9=\left(1 \times 9^3\right)+\left(8 \times 9^2\right)+\left(2 \times 9^1\right)+\left(3 \times 9^0\right) $$
$$ \begin{aligned} &\text { Hasil tambah nilai digit } 8 \text { dan nilai digit } 3\\ &\begin{aligned} & =\left(8 \times 9^2\right)+\left(3 \times 9^0\right) \\ & =648+3 \\ & =651 \end{aligned} \end{aligned} $$
Soalan 9:
Susun nombor berikut mengikut urutan menaik.
$$ \text { (a) } 110_2, 1101_2, 111_2, 1110_2 $$
$$ \text { (b) } 1123_4, 132_4, 231_4, 112_4 $$
$$ \text { (c) } 324_5, 124_5, 241_5, 231_5 $$
Penyelesaian:
(a)
$$ \begin{aligned} 110_2 & =\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(0 \times 2^0\right) \\ & =4+2 \\ & =6 \end{aligned} $$
$$ \begin{aligned} 1101_2 & =\left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(0 \times 2^1\right)+\left(1 \times 2^0\right) \\ & =8+4+0+1 \\ & =13 \end{aligned} $$
$$ \begin{aligned} 111_2 & =\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right) \\ & =4+2+1 \\ & =7 \end{aligned} $$
$$ \begin{aligned} 1110_2 & =\left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(0 \times 2^0\right) \\ & =8+4+2+0 \\ & =14 \end{aligned} $$
$$ \text { Susun nombor mengikut urutan menaik }=110_2, 111_2, 1101_2, 1110_2 $$
(b)
$$ \begin{aligned} 1123_4 & =\left(1 \times 4^3\right)+\left(1 \times 4^2\right)+\left(2 \times 4^1\right)+\left(3 \times 4^0\right) \\ & =64+16+8+3 \\ & =91 \end{aligned} $$
$$ \begin{aligned} 132_4 & =\left(1 \times 4^2\right)+\left(3 \times 4^1\right)+\left(2 \times 4^0\right) \\ & =16+12+2 \\ & =30 \end{aligned} $$
$$ \begin{aligned} 231_4 & =\left(2 \times 4^2\right)+\left(3 \times 4^1\right)+\left(1 \times 4^0\right) \\ & =32+12+1 \\ & =45 \end{aligned} $$
$$ \begin{aligned} 112_4 & =\left(1 \times 4^2\right)+\left(1 \times 4^1\right)+\left(2 \times 4^0\right) \\ & =16+4+2 \\ & =22 \end{aligned} $$
$$ \text { Susun nombor mengikut urutan menaik }=112_4, 132_4, 231_4, 1123_4 $$
(c)
$$ \begin{aligned} 324_5 & =\left(3 \times 5^2\right)+\left(2 \times 5^1\right)+\left(4 \times 5^0\right) \\ & =75+10+4 \\ & =89 \end{aligned} $$
$$ \begin{aligned} 124_5 & =\left(1 \times 5^2\right)+\left(2 \times 5^1\right)+\left(4 \times 5^0\right) \\ & =25+10+4 \\ & =39 \end{aligned} $$
$$ \begin{aligned} 241_5 & =\left(2 \times 5^2\right)+\left(4 \times 5^1\right)+\left(1 \times 5^0\right) \\ & =50+20+1 \\ & =71 \end{aligned} $$
$$ \begin{aligned} 231_5 & =\left(2 \times 5^2\right)+\left(3 \times 5^1\right)+\left(1 \times 5^0\right) \\ & =50+15+1 \\ & =66 \end{aligned} $$
$$ \text { Susun nombor mengikut urutan menaik }=124_5, 231_5, 241_5, 324_5 $$
Susun nombor berikut mengikut urutan menaik.
$$ \text { (a) } 110_2, 1101_2, 111_2, 1110_2 $$
$$ \text { (b) } 1123_4, 132_4, 231_4, 112_4 $$
$$ \text { (c) } 324_5, 124_5, 241_5, 231_5 $$
Penyelesaian:
(a)
$$ \begin{aligned} 110_2 & =\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(0 \times 2^0\right) \\ & =4+2 \\ & =6 \end{aligned} $$
$$ \begin{aligned} 1101_2 & =\left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(0 \times 2^1\right)+\left(1 \times 2^0\right) \\ & =8+4+0+1 \\ & =13 \end{aligned} $$
$$ \begin{aligned} 111_2 & =\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right) \\ & =4+2+1 \\ & =7 \end{aligned} $$
$$ \begin{aligned} 1110_2 & =\left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(0 \times 2^0\right) \\ & =8+4+2+0 \\ & =14 \end{aligned} $$
$$ \text { Susun nombor mengikut urutan menaik }=110_2, 111_2, 1101_2, 1110_2 $$
(b)
$$ \begin{aligned} 1123_4 & =\left(1 \times 4^3\right)+\left(1 \times 4^2\right)+\left(2 \times 4^1\right)+\left(3 \times 4^0\right) \\ & =64+16+8+3 \\ & =91 \end{aligned} $$
$$ \begin{aligned} 132_4 & =\left(1 \times 4^2\right)+\left(3 \times 4^1\right)+\left(2 \times 4^0\right) \\ & =16+12+2 \\ & =30 \end{aligned} $$
$$ \begin{aligned} 231_4 & =\left(2 \times 4^2\right)+\left(3 \times 4^1\right)+\left(1 \times 4^0\right) \\ & =32+12+1 \\ & =45 \end{aligned} $$
$$ \begin{aligned} 112_4 & =\left(1 \times 4^2\right)+\left(1 \times 4^1\right)+\left(2 \times 4^0\right) \\ & =16+4+2 \\ & =22 \end{aligned} $$
$$ \text { Susun nombor mengikut urutan menaik }=112_4, 132_4, 231_4, 1123_4 $$
(c)
$$ \begin{aligned} 324_5 & =\left(3 \times 5^2\right)+\left(2 \times 5^1\right)+\left(4 \times 5^0\right) \\ & =75+10+4 \\ & =89 \end{aligned} $$
$$ \begin{aligned} 124_5 & =\left(1 \times 5^2\right)+\left(2 \times 5^1\right)+\left(4 \times 5^0\right) \\ & =25+10+4 \\ & =39 \end{aligned} $$
$$ \begin{aligned} 241_5 & =\left(2 \times 5^2\right)+\left(4 \times 5^1\right)+\left(1 \times 5^0\right) \\ & =50+20+1 \\ & =71 \end{aligned} $$
$$ \begin{aligned} 231_5 & =\left(2 \times 5^2\right)+\left(3 \times 5^1\right)+\left(1 \times 5^0\right) \\ & =50+15+1 \\ & =66 \end{aligned} $$
$$ \text { Susun nombor mengikut urutan menaik }=124_5, 231_5, 241_5, 324_5 $$