Binary Shifts

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Binary shifts. Binary shifts are when you move a binary number either places to the left or places to the right. When you do the same thing with a decimal number you are multiplying or dividing by powers of 10. And that's because decimal works in base 10. When you do this in binary as its base two, you're multiplying or dividing the number by powers of two. As can be seen in this example, we begin with the binary number 1100, which is the equivalent 12 in decimal.

If we shift this one place to the left, we end up with a number 1100. And we then have a space space which we must fill with another zero. Our final binary number therefore becomes 11000, which is the equivalent of 24 in decimal. As we can see, 12 times two is 24. So consequently, that Binary has been multiplied by two as we have shifted one place to the left. In this example, we begin with a binary number 1010010 which is equivalent to 82 in decimal, as we are shifting to the right, the one that was in the 64 position moves to the 32 position zero that was in the 32 position moves to the 16 position and so on.

We therefore end up with a binary number 101001 which is equivalent to 41 the binary number has been divided by two as we have shifted one place to the right. You may ask what happens to the zero that was originally in the one position for GCSE It is enough to consider this just falls off the end. If you study this topic at a more advanced level, you will be shown that there is a binary point numbers are then shifted into positions beyond this binary point. In this example, we start with the binary number 110, which is equivalent to six in decimal. This time, we're going to move the number two places to the left. And this means that it's going to get four times bigger.

One places two times bigger two places is four times bigger. As we can see, the one that was originally in the four position moves to the 16. The one that was in the two position moved to the eight, and the one that was in the zero moves to the four, we then got to blank spaces where we must add in extra zeros. Looking at a new binary number, we have 11000, which is equivalent to 24. in decimal, the original decimal number we have the six, we've now got 24, which is four times larger, or six times two times two. Every time you shift the binary number to the left by one place, it gets two times bigger every time you shift a binary number to the right again gets two times smaller. On this slide, it is possible to see the different rules for shifting left and shifting right.

Make sure you've had a good look at them before moving on. Here's a question for you to try. Given the binary number 1001, a form a binary, shift three places to the left, consider what your final binary number is, and then convert that into decimal. Pause the video wash you have a go at this. In this example, the original binary number of 100 or one has moved three places to the left giving a result of 1001000. This is equivalent 72 in decimal.

A three place shift multiplies the number by eight as each shift left is a multiplication of two. So two times two times two, which is eight. If we take the original decimal number of nine and multiply it by eight, we can See that we arrived at the same result of 72. Here we have another example for you to try. This time it's a three play shift to the right. Pause the video whilst you have a go.

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