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Fundamentals of Binary Arithmetic

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In this video we will understand binary numbers as the basic language of computers.

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Compare binary with decimal numbers and recognize their role in data.

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Learn the rules for performing binary addition with carries.

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Learn the rules for performing binary subtraction with borrowing.

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Everything a computer does comes down to just two numbers,

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one and zero.

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Today we'll explore binary arithmetic,

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how the simple digits perform calculations, store information,

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and power the technology we use every day.

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Binary is a numbering system where all possible values are represented by two symbols,

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such as on-off, true false, or one and zero.

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Computers handle all data as a stream of binary numbers

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and it is much easier to work with two values than ten values in a decimal system.

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Binary addition follows simple rules, adding zero and zero gives zero.

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Zero and one gives one.

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One and zero gives one.

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And one plus one gives ten.

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That's zero with a carry of one to the next column.

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Let's explain with example.

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So when we add these two digits one plus one, the sum will be zero,

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and carry to the next column will be one.

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So now let's add these two digits.

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One plus one, the sum will be zero,

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and carry to the next column will be one.

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Now here zero plus one gives us one.

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So that's how we can add these numbers together.

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Now let's come to the next column one plus one.

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The summation will be zero, and carry to the next column will be one.

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0 plus 0 is 0. Now let's jump to the next column. 1 plus 0 is 1 and 1 plus 1 is 0.

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And carry to the next column is 1. Now again over here 1 plus 1. The sum is 0. And carry

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to the next column will be 1. Now 0 plus 1 gives us 1. Now here we have 1 carry. But no

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digit is available into this numbers. So by default we will take it as 1. So that is

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how you can add 2 binary numbers. Let's understand binary subtraction. Binary

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subtraction follow these rules. 0 minus 0 gives 0. 1 minus 0 gives 1. 1 minus 1 gives 0.

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And when 0 minus 1 occurs we borrow from the next column. Let's subtract these 2 binary

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numbers step by step. We always begin from the rightmost column and move left. In the

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first column 1 minus 1 gives 0. In the next column we need to subtract 1 from 0. This

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isn't possible directly. So we borrow from the next column just like in decimal subtraction.

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In decimal borrowing increases the value by 10. In binary borrowing increases the value

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by 2. Which we write as 1 0. So when we borrow the 0 becomes 10. Now 10 minus 1 gives 1.

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Moving on 0 minus 0 is 0. And finally 1 minus 1 is 0. That's how binary subtraction