homework quiz 8: digital electronics
score: 0/15 answered: 0/15
question 1
convert the following hexadecimal number (base 16) to decimal (base 10):
6a48₁₆ = (base 10)
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question 2
convert the following binary number to decimal (base 10):
11001100₂ = (base 10)
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question 3
convert the following octal number (base 8) to decimal (base 10).
610060₈ =

Question

Accepted Answer

# Explanation:
## Step1: Hexadecimal to Decimal Conversion
In hexadecimal, $A = 10$ in decimal.
$$
\begin{align*}
6A48_{16}&=6\times16^{3}+10\times16^{2}+4\times16^{1}+8\times16^{0}\
&=6\times4096 + 10\times256+4\times16 + 8\times1\
&=24576+2560 + 64+8
\end{align*}
$$
## Step2: Binary to Decimal Conversion
$$
\begin{align*}
11001100_{2}&=1\times2^{7}+1\times2^{6}+0\times2^{5}+0\times2^{4}+1\times2^{3}+1\times2^{2}+0\times2^{1}+0\times2^{0}\
&=128 + 64+0+0 + 8+4+0+0\
&=204
\end{align*}
$$
## Step3: Octal to Decimal Conversion
$$
\begin{align*}
610060_{8}&=6\times8^{5}+1\times8^{4}+0\times8^{3}+0\times8^{2}+6\times8^{1}+0\times8^{0}\
&=6\times32768+1\times4096+0+0+6\times8+0\
&=196608+4096+48\
&=200752
\end{align*}
$$

# Answer:
1. $27208$
2. $204$
3. $200752$

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QUESTION IMAGE

Question

Explanation:

Step1: Hexadecimal to Decimal Conversion

Step2: Binary to Decimal Conversion

Step3: Octal to Decimal Conversion

Answer: