2 Marks Questions

Question 12 Marks

$(108)_{16}=(?)_{10}$

Answer

(vi) $(108)_{16}$
$\begin{array}{lll}\text { Digits } & 1 & 0 & 8\end{array}$
$\begin{array}{llll}\text { Position Number } & 2 & 1 & 0\end{array}$
$\begin{array}{lccc}\text { Position Value } & 16^2 & 16^1 & 16^0 \\ \text { Decimal Value } & 1 \times 16^2 & 0 \times 16^1 & 8 \times 16^0\end{array}$
$\begin{array}{l}=256+0+8 \\ =264\end{array}$
Thus, $\quad(108)_{16}=(264)_{10}$

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Question 22 Marks

$(798)_{10}=(?)_{16}$

Answer

(v) $(789)_{10}$
To change decimal into hexadecimal, we divide given decimal number repeatedly by 16 .

Thus, $\quad(789)_{10}=(315)_{16}$

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Question 32 Marks

$(889)_{10}=(?)_8$

Answer

(iv) $(889)_{10}$
To change decimal number into octal number, the decimal number is repeatedly divided by 8 .

Thus, $\quad(889)_{10}=(1571)_8$

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Question 42 Marks

$(76 F)_{16}=(?)_8$

Answer

(iii) $(76 F)_{16}$
$\begin{array}{cccc}\text { Hexadecimal Digits } & 7 & 6 & \text { F } \\ & \downarrow & \downarrow & \downarrow \\ & 0111 & 0110 & 1111\end{array}$
Now, group these digits from right to left in 3-bit form

Thus, $\quad(76 F)_{10}=(3557)_8$

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Question 52 Marks

$(220)_8=(?)_2$

Answer

(ii) $(220)_8$
Octal Digits 2 2 0
3-bit binary digit 010 010 000
Thus, $\quad(220)_8=(010010000)_2$

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Question 62 Marks

$(514)_8=(?)_{10}$

Answer

(i) (514) 8
$\begin{array}{llll}\text { Digit } & 5 & 1 & 4\end{array}$
$\begin{array}{llll}\text { Position Number } & 2 & 1 & 0\end{array}$
$\begin{array}{llll}\text { Positional Value } & 8^2 & 8^1 & 8^0\end{array}$
Decimal Number $\quad 5 \times 8^2 \quad 1 \times 8^1 \quad 4 \times 8^0$
$\begin{array}{l}=5 \times 64+1 \times 8+4 \times 1 \\ =320+8+4=332\end{array}$
Hence, $\quad(514)_8=(332)_{10}$

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Question 72 Marks

Multiply $(1011.01)_2$ to $(110.1)_2$.

Answer

$\begin{array}{r}1011.01 \\ \hline \times \quad 110.1 \\ 101101 \\ 000000 \times \\ 101101 \times \times \\ \hline 101101 \times \times \times \\ \hline 1001001.001\end{array}$
Hence, $(1011.01)_2 \times(110.1)_2=(1001001.001)_2$

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Question 82 Marks

Convert $(10101100.010111)_2$ to hexadecimal.

Answer

Making perfect group of $\overline{1010} \quad \overline{1100} \quad . \overline{0101} \quad \overline{1100}$ 4 bits
Writing hexadecimal A C . 5 C
symbol foe each group
Therefore, $(10101100.010111)_2=( AC .5 C )_{16}$

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Question 92 Marks

Divide $(1001011)_2$ by $(11)_2$

Answer

Hence, quotient is $(11001)_2$.

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Question 102 Marks

Convert $(0.675)_{10}$ to binary.

Answer

Since, the fraction part ( 0.400 ) is the repeating value in the calculation, the multiplication is stopped.
Now, we have to write the integral part from top to bottom to get binary number for the given fraction part.
Therefore, $\quad(0.675)_{10}=(0.1010110)_2$

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Question 112 Marks

Find Decimal equivalent of Binary Number $(1011.011)_2$

Answer

Binary to Decimal conversion is obtained by multiplying 2 to the power of base index along with the value at that index position.
$\begin{array}{lcccccccc}\text { Digit } & 1 & 0 & 1 & 1 & . & 0 & 1 & 1 \\ \text { Fractional Value} & 2^3 & 2^2 & 2^1 & 2^0 & . & 2^{-1} & 2^{-2} & 2^{-3}\end{array}$
$\begin{array}{l}\text { Decimal value} \quad\quad 1 \times 2^3 0 \times 2^2 1 \times 2^1 1 \times 2^0 .0 \times 2^{-1} 1 \times 2^{-2}
\\=8+0+2+1.0+0.25+0.125 \\ =11.375 \\ \text { Hence, } \quad(1011.011)_2=(11.375)_{10}\end{array}$

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Question 122 Marks

Find decimal equivalent of the octal number $(645)_8$.

Answer

Octal to Decimal conversion is obtained by multiplying 8 to the power of base index along with the value at that index portion.
The decimal equivalent of the octal number $(648)_8$ is
Given digits $\begin{array}{lll}6 &\ 4 &\ 8\end{array}$
Position Number $\begin{array}{lll}2 &\ 1 &\ 0\end{array}$
Decimal value $8^2 \quad 8^1 \quad 8^0$
$\begin{array}{ll}\text { Decimal Number } & 6 \times 8^2+4 \times 8^1+8 \times 8^0 \\ & =6 \times 64+4 \times 8+8 \times 1 \\ & =384+32+8 \\ & =424 \\ \text { Hence, } \quad(648)_8 & =(424)_{10}\end{array}$

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Applied Maths 2 Marks Questions

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