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Unformatted text preview: Because there isnt a symbol for 10, we reuse the same digits and rely on position. The rightmost digit reverts to 0, and there is a carry into the next position to the left. Thus 1 + 9 equals 10 in base 10. The rules of binary arithmetic are analogous, but we run out of digits much sooner. 0 + 1 is 1, and 1 + 1 is 0 with a carry. Then the same rule is applied to every column in a larger number, and the process continues until there are no more digits to add. The example below adds the binary values 101110 and 11011. The carry value is marked above each column in color. 11111 carry 101110 + 11011 1001001 We can convince ourselves that this answer is correct by converting both operands to base 10, adding them, and comparing the result. 101110 is 46, 11011 is 27, and the sum is 73. 101001 is 73 in base 10....
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This note was uploaded on 01/13/2011 for the course CSE 1550 taught by Professor Marianakant during the Fall '10 term at York University.
- Fall '10