How To Sign Extend Into Register

A quick post today, explaining the concept of binarysign extension. Imagine the scenario. Yous take been using a single byte to store values and now want to extend this to store larger numbers? What would you have to do to extend your original one-byte of information to now shop numbers using 2-bytes? This is where binary sign extension comes in.

In this post, nosotros're going to look at ii scenarios where sign extension is useful. The starting time, where your original number is an unsigned binary number and the 2nd where your existing number is a signed binary number.

Extending Unsigned Binary Numbers

The approach to extending an unsigned binary number is pretty simple. It's a single-step process:

To extend an unsigned binary number, take the $.25 from the original number and append as many additional $.25 of storage as are necessary to the almost meaning end of the original number. The value of each appended scrap is set to null.

Only to exist clear, let'south await at an example.

Imagine we have a number 01010101₂ and wanted to extend it to utilize two bytes of storage instead of only 1.

In line with our rule above, we append an additional 8 bits / 1 byte of storage to the nigh significant end of the number.

Our resulting number is therefore: 00000000 01010101_ii (The appended bits are in bold).

Easy huh? But what about signed binary numbers?

Extending a Signed Binary Number

As with extending unsigned binary numbers, the rules for extending a signed binary number are over again unproblematic, though with signed binary numbers there is a slight difference to the rule in social club to preserve the sign flake of our original number:

"When extending a signed binary number represented in Two's Complement, additional bits are appended to the most pregnant cease of the number existence extended. When appending these bits, each bit is set to the same state as the the nearly significant bit (the sign bit) of the number existence extended."

Again, it's probably easier to work through an example.

Imagine this time we start with an 8-bit signed number stored in Two's Complement format:i010 1100₂ (or -84_ten) and we want to extend it to utilise xvi-bits / ii-bytes of storage instead of just viii-bits / 1-byte.

As we do when we extend unsigned binary numbers we start by appending an boosted eight-bits to the most meaning side of our number (the left paw finish).

This fourth dimension though, instead of setting all the bits to zero, each of these new $.25 is set to the same value as the sign-scrap of the number we're extending (which may be nil for positive numbers or 1 for negative numbers).

In this case the sign scrap of the number is 1 so we set all the new bits we append to ane as well.

Our new issue is therefore: 1111 1111 1010 1100_ii (the bits in bold are the new ones we've added).

Every bit a side note, this new number remains aTwo'south Complement representation but notice how the sign bit is exactly the aforementioned sign as the original we had. In improver, if you walk through the steps you learnt in the previous mail service(about how to convert a 2'southward Complement number into decimal), you should too see that this new number still equals -84₁₀ (which is bonus!).

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