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Binary Addition

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In primary school we are taught to use long addition to sum numbers on paper. The practice relies on the concept of carrying digits to + other columns when the simple addition excedes 10. We can use the same technique to add binary numbers just instead of carrying when + exceding 10, we do this at 1. The best way to visualise this is with a couple of rules whenn carrying. First, when adding two 1s in a column, + the answer is 0 carry 1. Secondly, when adding three 1s in a column (from a previous carry), the answer is 1 carry 1.

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Binary Subtraction Using 2's Complement

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Subtraction in binary is a little hard as it is not as intuitive as the addition. To subtract two binary numbers we use a method known as + 2's complement. 2's complement is a way of expressing a binary number as a negative. After doing this conversion, you can just add the two + numbers and it will give the same answer as if the two numbers were subtracted in denary. To find 2's complement, you begin by inverting + each bit in the number (if the bit is a 0 it becomes 1, and vice versa) and then add 1.