CODEWITHSUNDEEP
binarytype-conversioncomputer-science
Souza
Souza

Reputation: 1143

binary excess notation

i'm studying computer science and i can't figure something out of my own.

There is this number : -233 using 10 bit representation

What i need to do is to represent with excess notation the number (2^n-1)

So, i came up with:

1 base 10 = 0000000001

2^10-1 = 1000000000

1 base 10 in my notation = 1000000001

So, my -256 is 0000000001

And my 255 is 1111111110

What is the -233 number following this notation?

The result on the book is 0 1 0 0 0 1 0 1 1 1

My result: 0 0 0 0 0 1 0 1 1 1

Hope you guys can help me.

Upvotes: 0

Views: 3772

Answers (1)

Slomo
Slomo

Reputation: 1234

I think you were on the right path, but just did a small error.

As I was not familiar with the notation, I had to take a look at it first. It seems like K is usually chosen as 2^(n-1) = 2^9 = 512. Which means 00 0000 0000 = -512 and 11 1111 1111 = 511. I don't know how you get -256, maybe there is your error.

Now, from -512 (00 0000 0000) to -233 there is a difference of 279 (01 0001 0111). This seems to be the result of your example.

For easier construction you can do this (assuming K = 2^(n-1)) - example number -12:

  • Use the binary representation of the positive value (12). 00 0000 1100
  • Add K (2^(n-1)): 10 0000 1100
  • Invert all bits: 01 1111 0011
  • Add 1 (because of the zero value): 01 1111 0100

Upvotes: 1

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