1 1 1 1 0 1 1 0 X 1 1
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Binary multiplication:
I need to double check my answer
![### Binary Multiplication Example
Let's consider an example of binary multiplication. Below, we have two binary numbers which are going to be multiplied:
\[
\begin{array}{cccccc}
& 1 & 1 & 1 & 0 & 1 \\
\times & 1 & 1 & 0 & 1 \\
\end{array}
\]
### Explanation:
We will be multiplying the binary number \(11101_2\) by the binary number \(1101_2\).
1. Arrange the two binary numbers, one below the other, ensuring they are aligned to the right.
2. Start from the least significant bit (rightmost bit) of the bottom number and, for each bit, multiply it by the entire top number.
3. If the multiplier's bit is 1, write down the top number shifted to the left by the bit's position (starting from 0). If the bit is 0, write down 0s (of the same length as the top number shifted by the bit's position).
Here is a step-by-step breakdown of the multiplication:
1. **(Least Significant Bit on bottom number is 1):**
- Write down the top number shifted by 0 positions: \(11101_2\).
2. **(Next Bit 0):**
- Write down all 0's shifted by 1 position: \(00000_2\).
3. **(Next Bit 1):**
- Write down the top number shifted by 2 positions: \(1110100_2\).
4. **(Next Bit 1):**
- Write down the top number shifted by 3 positions: \(11101000_2\).
Now, add up the results obtained from the multiplications:
\[
\begin{array}{cccccccc}
& & & & 1 & 1 & 1 & 0 & 1 \\
+ & & & & 0 & 0 & 0 & 0 & 0 & 0 \\
+ & & & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\
+ & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\
&=&=&=&=&=&=&=&=&\\
& & 1 & 1 & 1 & 0 &](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec61610c-382a-4f8e-9761-46135314c956%2Fd5d36f76-bedf-4b02-ae58-a26d821a584d%2Fetq3wfp_processed.png&w=3840&q=75)
Transcribed Image Text:### Binary Multiplication Example
Let's consider an example of binary multiplication. Below, we have two binary numbers which are going to be multiplied:
\[
\begin{array}{cccccc}
& 1 & 1 & 1 & 0 & 1 \\
\times & 1 & 1 & 0 & 1 \\
\end{array}
\]
### Explanation:
We will be multiplying the binary number \(11101_2\) by the binary number \(1101_2\).
1. Arrange the two binary numbers, one below the other, ensuring they are aligned to the right.
2. Start from the least significant bit (rightmost bit) of the bottom number and, for each bit, multiply it by the entire top number.
3. If the multiplier's bit is 1, write down the top number shifted to the left by the bit's position (starting from 0). If the bit is 0, write down 0s (of the same length as the top number shifted by the bit's position).
Here is a step-by-step breakdown of the multiplication:
1. **(Least Significant Bit on bottom number is 1):**
- Write down the top number shifted by 0 positions: \(11101_2\).
2. **(Next Bit 0):**
- Write down all 0's shifted by 1 position: \(00000_2\).
3. **(Next Bit 1):**
- Write down the top number shifted by 2 positions: \(1110100_2\).
4. **(Next Bit 1):**
- Write down the top number shifted by 3 positions: \(11101000_2\).
Now, add up the results obtained from the multiplications:
\[
\begin{array}{cccccccc}
& & & & 1 & 1 & 1 & 0 & 1 \\
+ & & & & 0 & 0 & 0 & 0 & 0 & 0 \\
+ & & & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\
+ & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\
&=&=&=&=&=&=&=&=&\\
& & 1 & 1 & 1 & 0 &
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