Convert 100100112 to decimal.

Question

Convert [latex]10010011_{2}[/latex] to decimal.

Accepted Answer

Step 1: Write down the binary number, leaving space between the bits.
[latex]\begin{matrix} 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \end{matrix}[/latex]
Step 2: Double the high-order bit and copy it under the next bit.
[latex]\begin{matrix} 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \ & 2 & & & & & & \\frac{ imes 2}{2} & & & & & & & \end{matrix}[/latex]

Step 3: Add the next bit and double the sum. Copy this result under the next bit.

[latex]\begin{matrix} 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \ & 2 & 4 & & & & &\ & \frac{+0}{2}\\\frac{ imes 2}{2} & \frac{ imes 2}{4} & & & & & & \end{matrix}[/latex]

Step 4: Repeat Step 3 until you run out of bits.

[latex]\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 ext{The answer} : 10010011_{2} = 147_{10} \ \ \frac{ imes 2}{2} & \frac{ imes 2}{4} & \frac{ imes 2}{8} & \frac{ imes 2}{18} & \frac{ imes 2}{36} & \frac{ imes 2}{72} & \frac{ imes 2}{146} \end{matrix} [/latex]

When we combine hextet grouping (in reverse) with the double-dabble method, we find that we can convert hexadecimal to decimal with ease.

Question 2.1: Convert 100100112 to decimal.

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