I keep making carry mistakes when adding binary numbers in my notebook. Can someone walk through 1011 + 110 carefully so I understand the carrying rule?
Binary addition uses four simple rules: 0+0=0, 0+1=1, 1+0=1, and 1+1=10, meaning write 0 and carry 1. Align the numbers from the right: 1011 and 0110. Add column by column from the right. Rightmost: 1+0=1. Next: 1+1=10, write 0 carry 1. Next: 0+1=1, plus the carried 1 gives 10, write 0 carry 1. Next: 1+0=1, plus the carried 1 gives 10, write 0 carry 1. That final carry 1 goes to a new leftmost column. Reading the result top to bottom gives 10001. You can verify: 1011 is 11 and 110 is 6 in decimal, and 11+6=17, which is 10001 in binary. So the carry rule is the same as decimal, you just carry whenever a column reaches 2.
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