Countersign Binary Made Easy

Countersign binary

[Music] [Applause] [Music] [Applause] [Music] [Applause] [Music] hey john here let's talk about sign in zero extending binary numbers now the way we do this uh well first of all this is a section of this risk 5 assembly language programming manual i'm working on some day i might actually finish it i'm in section 2.3 so we go to the table of contents here and find 2.3 sign in zero extension that's where i'm at you don't have your own copy then go to google and type in rv alp i wouldn't be surprised if i'm the first one there i am okay there you go that's how you can find your own copy go over here to releases and github and scroll down to assets there's a book pdf that's what you're looking at right now those are the notes that i'm using okay all right so what is this all about if you have a binary number okay so these are binary values you can see the ones and zeros here and it is a signed two's complement number you can easily make a short number into a bigger number okay if that's what you want if you have a four bit binary number you can turn it into what looks like an eight bit number here or i don't know how many bits this is or maybe 32 however many this is you can take the signed bit and the most significant bit of the number and then just replicate it as many times as you want to put as many bits over here to the left without changing the magnitude of what the two's complement value represented in the first place right that's not a problem what if it's a positive number again two's complement it's the sign bit remember you're replicating the sign bit when you're adding more bits over here so no matter how many zeros there are to the left of this value it's still going to be 12 in decimal right 8 plus 4 is 12. so it's 12 here it's 12 here and down here as well just like these are all negative ones up here all right so in conclusion any signed number can have any quantity of additional most significant bits added to it it could be extended to any size provided that they repeat the value of the sign bit that you had when you started all right now this is obviously a work in progress i got some diagrams down here that a little bit nicer that talk about here is the most significant bit with a little marker in there and you can clearly see that they're extended to the left okay here's an example of a positive one uh whatever the value of this is and a 20-bit value if you took the sign bit here and replicated as many additional bits as you wanted you could convert a 20-bit value to a 32-bit value like this all right now that's all fine and dandy what if the value is not a two's complement binary number what if it's an unsigned binary number in other words what happens if this is uh represents 15 rather than negative one right if i'm interpreting this four bit pattern as an unsigned number the value would be 15. just like up here if i was interpreting this four bit number as a signed value would be negative one so what do you do here well if it's unsigned you cannot just replicate what would be this signed bit to the left simply because it's unsigned it has no signed bit so if you want to make this in a four bit number into a 32-bit number you use what's called zero extension all right so any unsigned number may be zero extended to any size all right and again here's some more diagrams of what it looks like in a little note to myself remove the sign bit boxes all right yeah i gotta get around to fixing these pictures someday so uh you do not replicate this bit when you're dealing with an unsigned number right you can clearly see in this example the the the original value is stays here and any additional bits are zeros and that works the same way in decimal as well right i mean this should be intuitive what's new perhaps is this idea that you would use sign extension this this this replicating of the signed bit all right do a couple on paper to confirm that it works for you like it does for everyone else all right so that's all there is to extending binary numbers both signed and unsigned thanks for watching have fun bye you