Question 2.1: Convert 100100112 to decimal.
Convert 10010011_{2} to decimal.
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Step 1: Write down the binary number, leaving space between the bits.
\begin{matrix} 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \end{matrix}
Step 2: Double the high-order bit and copy it under the next bit.
\begin{matrix} 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \\ & 2 & & & & & & \\\frac{\times 2}{2} & & & & & & & \end{matrix}
Step 3: Add the next bit and double the sum. Copy this result under the next bit.
Step 4: Repeat Step 3 until you run out of bits.
\begin{matrix} 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \\ & 2 & 4 & 8 & 18 & 36 & 72 & 146\\ \\ &\frac{+0}{2} & \frac{+0}{4} & \frac{+1}{9} & \frac{+0}{18} & \frac{+0}{36} & \frac{+1}{73} & \frac{+1}{147} & \Leftarrow \text{The answer} : 10010011_{2} = 147_{10} \\ \\ \frac{\times 2}{2} & \frac{\times 2}{4} & \frac{\times 2}{8} & \frac{\times 2}{18} & \frac{\times 2}{36} & \frac{\times 2}{72} & \frac{\times 2}{146} \end{matrix}When we combine hextet grouping (in reverse) with the double-dabble method, we find that we can convert hexadecimal to decimal with ease.
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