87 lines
1.3 KiB
Markdown
87 lines
1.3 KiB
Markdown
---
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tags:
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- binary
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---
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# Binary addition
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- We add binary values in columns just like we would with denary addition.
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- Each column is classified on the basis of place-value. In denary this is 10,
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in binary it is 2.
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- When we conduct a binary addition, we add the binary values as if they were
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normal integers but we represent the sums as binary.
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- For example: $1 + 1 = 2$ for the calculation but the sum is $10$
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## Examples
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### Example one
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$$
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1010 + 0111 = 10001
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$$
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$$
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10 + 7 = 17
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$$
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In the first column: $1 + 0 = 1$, so we simply put the binary value for $1$:
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```
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1010
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0111
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____
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1
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```
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In the second column: $1 + 1 = 2$. In binary this is represented as $10$. So we
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put $0$ beneath the bar and carry the $1$:
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```
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1
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1010
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0111
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____
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01
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```
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In the third column, we repeat the previous process. We are presented with
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$1 + 0 + 1$ which is $2$. As $2$ is $10$ in binary, we put the zero beneath the
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line and carry the $1$:
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```
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11
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1010
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0111
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____
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001
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```
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In the final column, we again have $1+1$ giving us $2$ or $10$ but at this point
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we cannot carry any more because we have reached the final column. So instead of
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carrying the $1$ we just put both digits beneath the line $10$.
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```
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11
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1010
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0111
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_____
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10001
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```
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### Example two
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$$
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1001 + 0111 = 10000
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$$
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$$
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9 + 7 = 16
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$$
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```
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111
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1001
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0111
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_____
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10000
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```
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