Soalan 6:
Tentukan nilai nombor berikut dalam asas sepuluh.
Penyelesaian:
(a) 236
$$ \begin{aligned} \text { Nilai nombor } & =\left(2 \times 6^1\right)+\left(3 \times 6^0\right) \\ & =12+3 \\ & =15 \end{aligned} $$
(b) 4258
$$ \begin{aligned} \text { Nilai nombor } & =\left(4 \times 8^2\right)+\left(2 \times 8^1\right)+\left(5 \times 8^0\right) \\ & =256+16+5 \\ & =277 \end{aligned} $$
(c) 1101012
$$ \begin{aligned} \text { Nilai nombor }= & \left(1 \times 2^5\right)+\left(1 \times 2^4\right)+\left(0 \times 2^3\right)+\left(1 \times 2^2\right)+ \\ & \left(0 \times 2^1\right)+\left(1 \times 2^0\right) \\ = & 32+16+0+4+0+1 \\ = & 53 \end{aligned} $$
(d) 3389
$$ \begin{aligned} \text { Nilai nombor } & =\left(3 \times 9^2\right)+\left(3 \times 9^1\right)+\left(8 \times 9^0\right) \\ & =243+27+8 \\ & =278 \end{aligned} $$
(e) 3647
$$ \begin{aligned} \text { Nilai nombor } & =\left(3 \times 7^2\right)+\left(6 \times 7^1\right)+\left(4 \times 7^0\right) \\ & =147+42+4 \\ & =193 \end{aligned} $$
(f) 334
$$ \begin{aligned} \text { Nilai nombor } & =\left(3 \times 4^1\right)+\left(3 \times 4^0\right) \\ & =12+3 \\ & =15 \end{aligned} $$
(g) 1235
$$ \begin{aligned} \text { Nilai nombor } & =\left(1 \times 5^2\right)+\left(2 \times 5^1\right)+\left(3 \times 5^0\right) \\ & =25+10+1 \\ & =38 \end{aligned} $$
(h) 12178
$$ \begin{aligned} \text { Nilai nombor } & =\left(1 \times 8^3\right)+\left(2 \times 8^2\right)+\left(1 \times 8^1\right)+\left(7 \times 8^0\right) \\ & =512+128+8+7 \\ & =655 \end{aligned} $$
(i) 5156
$$ \begin{aligned} \text { Nilai nombor } & =\left(5 \times 6^2\right)+\left(1 \times 6^1\right)+\left(5 \times 6^0\right) \\ & =180+6+5 \\ & =191 \end{aligned} $$
(j) 11213
$$ \begin{aligned} \text { Nilai nombor } & =\left(1 \times 3^3\right)+\left(1 \times 3^2\right)+\left(2 \times 3^1\right)+\left(1 \times 3^0\right) \\ & =27+9+6+1 \\ & =43 \end{aligned} $$
Tentukan nilai nombor berikut dalam asas sepuluh.
Penyelesaian:
(a) 236
$$ \begin{aligned} \text { Nilai nombor } & =\left(2 \times 6^1\right)+\left(3 \times 6^0\right) \\ & =12+3 \\ & =15 \end{aligned} $$
(b) 4258
$$ \begin{aligned} \text { Nilai nombor } & =\left(4 \times 8^2\right)+\left(2 \times 8^1\right)+\left(5 \times 8^0\right) \\ & =256+16+5 \\ & =277 \end{aligned} $$
(c) 1101012
$$ \begin{aligned} \text { Nilai nombor }= & \left(1 \times 2^5\right)+\left(1 \times 2^4\right)+\left(0 \times 2^3\right)+\left(1 \times 2^2\right)+ \\ & \left(0 \times 2^1\right)+\left(1 \times 2^0\right) \\ = & 32+16+0+4+0+1 \\ = & 53 \end{aligned} $$
(d) 3389
$$ \begin{aligned} \text { Nilai nombor } & =\left(3 \times 9^2\right)+\left(3 \times 9^1\right)+\left(8 \times 9^0\right) \\ & =243+27+8 \\ & =278 \end{aligned} $$
(e) 3647
$$ \begin{aligned} \text { Nilai nombor } & =\left(3 \times 7^2\right)+\left(6 \times 7^1\right)+\left(4 \times 7^0\right) \\ & =147+42+4 \\ & =193 \end{aligned} $$
(f) 334
$$ \begin{aligned} \text { Nilai nombor } & =\left(3 \times 4^1\right)+\left(3 \times 4^0\right) \\ & =12+3 \\ & =15 \end{aligned} $$
(g) 1235
$$ \begin{aligned} \text { Nilai nombor } & =\left(1 \times 5^2\right)+\left(2 \times 5^1\right)+\left(3 \times 5^0\right) \\ & =25+10+1 \\ & =38 \end{aligned} $$
(h) 12178
$$ \begin{aligned} \text { Nilai nombor } & =\left(1 \times 8^3\right)+\left(2 \times 8^2\right)+\left(1 \times 8^1\right)+\left(7 \times 8^0\right) \\ & =512+128+8+7 \\ & =655 \end{aligned} $$
(i) 5156
$$ \begin{aligned} \text { Nilai nombor } & =\left(5 \times 6^2\right)+\left(1 \times 6^1\right)+\left(5 \times 6^0\right) \\ & =180+6+5 \\ & =191 \end{aligned} $$
(j) 11213
$$ \begin{aligned} \text { Nilai nombor } & =\left(1 \times 3^3\right)+\left(1 \times 3^2\right)+\left(2 \times 3^1\right)+\left(1 \times 3^0\right) \\ & =27+9+6+1 \\ & =43 \end{aligned} $$
Soalan 7:
Tentukan nilai p dan nilai q.
$$ \text { (a) } 1101_2=\left(1 \times 2^p\right)+(1 \times q)+\left(1 \times 2^0\right) $$
$$ \text { (b) } 375_8=\left(3 \times 8^p\right)+\left(q \times 8^1\right)+\left(5 \times 8^0\right) $$
$$ \text { (c) } 1321_4=\left(1 \times p^q\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right) $$
Penyelesaian:
(a)
$$ 1101_2=\left(1 \times 2^p\right)+(1 \times q)+\left(1 \times 2^0\right) $$
$$ \left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(1 \times 2^0\right)=\left(1 \times 2^p\right)+(1 \times q)+\left(1 \times 2^0\right) $$
$$ \begin{aligned} &\text { Secara bandingan, }\\ &\begin{array}{rlrl} 2^3 & =2^p & 2^2 & =q \\ p & =3 & q & =2^2 \end{array} \end{aligned} $$
(b)
$$ 375_8=\left(3 \times 8^p\right)+\left(q \times 8^1\right)+\left(5 \times 8^0\right) $$
$$ \left(3 \times 8^2\right)+\left(7 \times 8^1\right)+\left(5 \times 8^0\right)=\left(3 \times 8^p\right)+\left(q \times 8^1\right)+\left(5 \times 8^0\right) $$
$$ \begin{aligned} &\text { Secara bandingan, }\\ &\begin{array}{rlr} 8^2 & =8^p & q=7 \\ p & =2 & \end{array} \end{aligned} $$
(c)
$$ 1321_4=\left(1 \times p^q\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right) $$
$$ \begin{aligned} & \left(1 \times 4^3\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right)= \\ & \left(1 \times p^q\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right) \end{aligned} $$
$$ \begin{aligned} &\text { Secara bandingan, }\\ &\begin{aligned} 4^3 & =p^q \\ p & =4 \\ q & =3 \end{aligned} \end{aligned} $$
Tentukan nilai p dan nilai q.
$$ \text { (a) } 1101_2=\left(1 \times 2^p\right)+(1 \times q)+\left(1 \times 2^0\right) $$
$$ \text { (b) } 375_8=\left(3 \times 8^p\right)+\left(q \times 8^1\right)+\left(5 \times 8^0\right) $$
$$ \text { (c) } 1321_4=\left(1 \times p^q\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right) $$
Penyelesaian:
(a)
$$ 1101_2=\left(1 \times 2^p\right)+(1 \times q)+\left(1 \times 2^0\right) $$
$$ \left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(1 \times 2^0\right)=\left(1 \times 2^p\right)+(1 \times q)+\left(1 \times 2^0\right) $$
$$ \begin{aligned} &\text { Secara bandingan, }\\ &\begin{array}{rlrl} 2^3 & =2^p & 2^2 & =q \\ p & =3 & q & =2^2 \end{array} \end{aligned} $$
(b)
$$ 375_8=\left(3 \times 8^p\right)+\left(q \times 8^1\right)+\left(5 \times 8^0\right) $$
$$ \left(3 \times 8^2\right)+\left(7 \times 8^1\right)+\left(5 \times 8^0\right)=\left(3 \times 8^p\right)+\left(q \times 8^1\right)+\left(5 \times 8^0\right) $$
$$ \begin{aligned} &\text { Secara bandingan, }\\ &\begin{array}{rlr} 8^2 & =8^p & q=7 \\ p & =2 & \end{array} \end{aligned} $$
(c)
$$ 1321_4=\left(1 \times p^q\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right) $$
$$ \begin{aligned} & \left(1 \times 4^3\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right)= \\ & \left(1 \times p^q\right)+\left(3 \times 4^2\right)+\left(2 \times 4^1\right)+\left(1 \times 4^0\right) \end{aligned} $$
$$ \begin{aligned} &\text { Secara bandingan, }\\ &\begin{aligned} 4^3 & =p^q \\ p & =4 \\ q & =3 \end{aligned} \end{aligned} $$