Answer:
0110 = 6 (base 10) 0111 = 7 (base 10) 1101 = 13 (base 10)
0110 = 6 (base 10) 0111 = 7 (base 10) 1101 = 13 (base 10)
Here is another example. Observe that the binary addition algorithm is the same algorithm you use with ordinary base ten addition, except now the base two addition table is used for each column.
0110 1110
0001 0111
|
0
0110 1110
0001 0111
1
|
10
0110 1110
0001 0111
01
|
110
0110 1110
0001 0111
101
|
1 110
0110 1110
0001 0111
0101
|
|
11 110 0110 1110 0001 0111 0 0101 |
111 110 0110 1110 0001 0111 00 0101 |
1111 110 0110 1110 0001 0111 000 0101 |
01111 110 0110 1110 0001 0111 1000 0101 |
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The carry out of the left column in the final sum can be discarded, in this case. But in general you must be careful with it. See the following pages. | |||||
Check the answer by converting to decimal representation and doing the addition in that base (the same numbers are being added, but now represented in a different way, so the sum is the same.)
01111 110
0110 1110 = 110 (base 10)
+ 0001 0111 = 23 (base 10)
1000 0101 = 133 (base 10)
This would be a good time to play with the Binary Addition Calculator applet in Appendix E.
Do the following:
10
+ 01