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By the end of this worksheet you should: • know how a computer adds two binary values together. • be able to define what is meant by a carry.
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By the end of this worksheet you should:
Again, this is obvious but we also know that computers only use binary (zeros and ones), so there is no 2 or 3. Instead, we need to use the binary equivalent values for 2 and 3, which are: 0 00 1 01 2 10 3 11 And then we need to remember the old carry we do in our own mathematics. Carry? Consider adding these two denary values together: 2 5 1 1 7 5 4 2 6 1 Look at the small 1 at the bottom of the last column; that is a carry. This is there because when we add 5 and 7 together we get a value bigger than 9; so, we need to carry the tens part of the answer into the next column. CARRY : to transfer to the next column. In maths, if the result of a calculation exceeds the maximum value for that column, the additional amount is ‘carried over’ to the next, more significant, column. We do the same in binary: (^0 1 0 1 1 0 0 ) (^0 0 1 1 0 1 0 ) 1 0 0 0 1 1 1 0 1 1 1 1
Try these… a) 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 b) 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 1 c) 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 d) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 e) 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 f) 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1