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Curry
 one year ago
Can someone check my answer for this binary combo question?
Curry
 one year ago
Can someone check my answer for this binary combo question?

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Curry
 one year ago
Best ResponseYou've already chosen the best response.11. [2^(n1)+1, 2^n1] 2. [2^(n1)+1, 2^n1]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Let \(n\) = 8 bits whats the largest positive number in 1's complement system ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes, \(\large 2^71\) is the largest number in 1's complement system using 8 bits : \[\large 2^71~~=~~0111 ~1111\]

Curry
 one year ago
Best ResponseYou've already chosen the best response.1wait, actually i'm kinda confused about that to begin with.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3what exactly are you confused about ?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1so, if i have 0000 0000, in one's compliment, cant i write 1111 1111?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3thats the reason 1's complement system sucks, we have two different representations for 0 in this system : ``` 0000 0000 ``` and ``` 1111 1111 ``` both represent the same number 0 in this system

Curry
 one year ago
Best ResponseYou've already chosen the best response.1oh ok, so 1 is the smallest number i can write that can be converted to one's complement so that it bcomes the largest?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3I don't get you, could you elaborate a bit

Curry
 one year ago
Best ResponseYou've already chosen the best response.1since i'm flipping the bits, the smallest number i write in binary would give me the greatest number in one's complement right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you don't flip bits when the left most bit is 0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you flip only when the left most bit is 1

Curry
 one year ago
Best ResponseYou've already chosen the best response.1oh beacuse it's positive?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1so one's complement only works when we're dealing with signed magnitude numbers?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3signed magnitude has nothing to do with 1's complement

Curry
 one year ago
Best ResponseYou've already chosen the best response.1well unsigned is always positive isn't it?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1so it has to be a negative number for one's complement to have an effect right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3You maybe correct but I'm not getting you First notice that "one's complement of a number" and "ones complement system" are two different things

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3In "one's complement system", binary strings with 0 as left most bit are treated as positive binary strings with 1 as left most bit are treated as negative

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3for example, `010 0000` is a positive number because the left most bit is `0` `1000 0000` is a negative number because the left most bit is `1`

Curry
 one year ago
Best ResponseYou've already chosen the best response.1so how is it different frmo signed magnitude system?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1isnn't signed magnitude the same thing? where 0 is positive and 1 is negative?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3before answering that, let me ask you two simple questions : what are the values of `0100 0000` in 1's complement and signed magnitude ? what are the values of `1000 0000` in 1's complement and signed magnitude ?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1for the first one: one complement = 0100 0000 signed magnitude = 64 second one: one complement = 1111 1111 signed magnitude = 0 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3tell me all the values in decimal form

Curry
 one year ago
Best ResponseYou've already chosen the best response.1for the first one it'll be 64 both times. second: 64, 0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you're correct about first one being 64 in both systems second one is wrong, try again

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3what are the values of `1000 0000` in 1's complement and signed magnitude ? #1's complement system : since the left most bit is `1`, we need to take 1's complement of this for the value and put minus sign. 1's complement = 0111 1111 = 127 so the value is \(\large 127\) #signed magnitude system : since the left most bit is `1`, the value is simply \(\large 0\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3so what do you notice ? what exactly is the difference between '"ones complement system" and "signed magnitude system" ?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1well just with respect to the left most bit, it's the same for positive numbers.

Curry
 one year ago
Best ResponseYou've already chosen the best response.1OOO! so if i have a binary number, and if it's positive, for one/two complement and signed magnitude, it'll be the same.

Curry
 one year ago
Best ResponseYou've already chosen the best response.1if there is a one in front of the binary, then i flip all the bits, calculate new decimal value, and add negative number.

Curry
 one year ago
Best ResponseYou've already chosen the best response.1and for two's compliment, i write teh number as positive first, flip all the bits, and add 1.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3coming back the original question, whats the smallest number in 1's complement system using 8 bits ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes \[127 = 1000~0000\] this is the smallest number in 1's complement system using 8 bits

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3using \(8\) bits, it seems we can express the numbers from \((2^{7}1)\) to \(2^71\) ?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1so for the biggest number would it be, 1111 1110?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3left most bit = 1, so thats a negative number think a bit, how can a negative number be the biggest ?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1no 1111 1110 is in one's complement. so in just binary, it'd be 0000 0001.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3how do you say 1 is the biggest number ?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1so if it doesn't matter when it's a positive number, would it be 0111 1111, which is 128?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3thats right, 127 is the biggest number using 8 bits in 1's complement system

Curry
 one year ago
Best ResponseYou've already chosen the best response.1oh so it's just that simple? 1111 1111 , 0111 1111?

Curry
 one year ago
Best ResponseYou've already chosen the best response.1How would I do it for tw's complement? or should i post this as a new question?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3wait, ``` oh so it's just that simple? 1111 1111 , 0111 1111? ``` what are you trying to say here

Curry
 one year ago
Best ResponseYou've already chosen the best response.1so in one's complement, to find the greatest and smallest number given n bits, it's always 2^(n1) 1

Curry
 one year ago
Best ResponseYou've already chosen the best response.1wait positive and negative 2^(n1) 1.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3thats right, but what has that do with `1111 1111 ` ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3`1111 1111 ` = 0 right

Curry
 one year ago
Best ResponseYou've already chosen the best response.1oh sorry, i meant 1000 0000.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3now that makes sense, yeah `1000 0000` is the least number and `0111 1111` is the max number in 1's complement system using 8 bits

Curry
 one year ago
Best ResponseYou've already chosen the best response.1oh ok, this makes a lot of sense now, thanks!!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3good, sry to ask too many questions but do you happen to know why signed magnitude is not so good for representing numbers in a computer ?
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