Curry
  • Curry
Can someone check my answer for this binary combo question?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Curry
  • Curry
1 Attachment
Curry
  • Curry
1. [-2^(n-1)+1, 2^n-1] 2. [-2^(n-1)+1, 2^n-1]
Curry
  • Curry
@wio

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Curry
  • Curry
@ganeshie8
ganeshie8
  • ganeshie8
Let \(n\) = 8 bits whats the largest positive number in 1's complement system ?
Curry
  • Curry
um, 2^8?
ganeshie8
  • ganeshie8
nope
Curry
  • Curry
wait no, 2^8 - 1
Curry
  • Curry
no no, 2^7 -1
ganeshie8
  • ganeshie8
Yes, \(\large 2^7-1\) is the largest number in 1's complement system using 8 bits : \[\large 2^7-1~~=~~0111 ~1111\]
Curry
  • Curry
wait, actually i'm kinda confused about that to begin with.
ganeshie8
  • ganeshie8
what exactly are you confused about ?
Curry
  • Curry
so, if i have 0000 0000, in one's compliment, cant i write 1111 1111?
ganeshie8
  • ganeshie8
thats 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
  • Curry
oh 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
  • ganeshie8
I don't get you, could you elaborate a bit
Curry
  • Curry
since i'm flipping the bits, the smallest number i write in binary would give me the greatest number in one's complement right?
ganeshie8
  • ganeshie8
you don't flip bits when the left most bit is 0
ganeshie8
  • ganeshie8
you flip only when the left most bit is 1
Curry
  • Curry
oh beacuse it's positive?
ganeshie8
  • ganeshie8
yes
Curry
  • Curry
so one's complement only works when we're dealing with signed magnitude numbers?
ganeshie8
  • ganeshie8
signed magnitude has nothing to do with 1's complement
Curry
  • Curry
well unsigned is always positive isn't it?
Curry
  • Curry
so it has to be a negative number for one's complement to have an effect right?
ganeshie8
  • ganeshie8
You 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
  • ganeshie8
In "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
  • ganeshie8
for 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
  • Curry
so how is it different frmo signed magnitude system?
Curry
  • Curry
isnn't signed magnitude the same thing? where 0 is positive and 1 is negative?
ganeshie8
  • ganeshie8
before 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
  • Curry
for the first one: one complement = 0100 0000 signed magnitude = 64 second one: one complement = 1111 1111 signed magnitude = 0 ?
ganeshie8
  • ganeshie8
tell me all the values in decimal form
Curry
  • Curry
for the first one it'll be 64 both times. second: -64, 0
ganeshie8
  • ganeshie8
you're correct about first one being 64 in both systems second one is wrong, try again
Curry
  • Curry
wait positive 64 and 0.
ganeshie8
  • ganeshie8
what 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
  • ganeshie8
so what do you notice ? what exactly is the difference between '"ones complement system" and "signed magnitude system" ?
ganeshie8
  • ganeshie8
http://gyazo.com/ee939ee2e32939bec143ee78b1d6afd1
Curry
  • Curry
well just with respect to the left most bit, it's the same for positive numbers.
Curry
  • Curry
OOO! 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
  • Curry
if there is a one in front of the binary, then i flip all the bits, calculate new decimal value, and add negative number.
Curry
  • Curry
and for two's compliment, i write teh number as positive first, flip all the bits, and add 1.
Curry
  • Curry
do i have this right?
ganeshie8
  • ganeshie8
Exactly!
ganeshie8
  • ganeshie8
coming back the original question, whats the smallest number in 1's complement system using 8 bits ?
Curry
  • Curry
-127?
ganeshie8
  • ganeshie8
Yes \[-127 = 1000~0000\] this is the smallest number in 1's complement system using 8 bits
ganeshie8
  • ganeshie8
using \(8\) bits, it seems we can express the numbers from \(-(2^{7}-1)\) to \(2^7-1\) ?
Curry
  • Curry
yes.
Curry
  • Curry
so for the biggest number would it be, 1111 1110?
ganeshie8
  • ganeshie8
left most bit = 1, so thats a negative number think a bit, how can a negative number be the biggest ?
Curry
  • Curry
no 1111 1110 is in one's complement. so in just binary, it'd be 0000 0001.
ganeshie8
  • ganeshie8
1111 1110 = -1
ganeshie8
  • ganeshie8
how do you say -1 is the biggest number ?
Curry
  • Curry
so if it doesn't matter when it's a positive number, would it be 0111 1111, which is 128?
Curry
  • Curry
sorry, 127.
ganeshie8
  • ganeshie8
thats right, 127 is the biggest number using 8 bits in 1's complement system
Curry
  • Curry
oh so it's just that simple? 1111 1111 , 0111 1111?
Curry
  • Curry
How would I do it for tw's complement? or should i post this as a new question?
ganeshie8
  • ganeshie8
wait, ``` oh so it's just that simple? 1111 1111 , 0111 1111? ``` what are you trying to say here
Curry
  • Curry
so in one's complement, to find the greatest and smallest number given n bits, it's always 2^(n-1) -1
Curry
  • Curry
wait positive and negative 2^(n-1) -1.
ganeshie8
  • ganeshie8
thats right, but what has that do with `1111 1111 ` ?
ganeshie8
  • ganeshie8
`1111 1111 ` = 0 right
Curry
  • Curry
oh sorry, i meant 1000 0000.
ganeshie8
  • ganeshie8
now 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
  • Curry
oh ok, this makes a lot of sense now, thanks!!
ganeshie8
  • ganeshie8
good, 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 ?
Curry
  • Curry
no, i don't. why?

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