# Basic Binary

1. Oct 2, 2013

### ccky

1. The problem statement, all variables and given/known data
Find the decimal values for the following 8-bit bit pattern
A)00000010 in excess 128 representation
B)10000010 in excess 128 2's complement representation
C)10000010 in excess 128 representation
2. Relevant equations
Binary
2's complement

3. The attempt at a solution
A(00000010)-1
(00000001)
=11111110.
=254-128=126

B)invert the number to 01111101 and+1=-126

C)130
Is it right or wrong?

Last edited: Oct 2, 2013
2. Oct 2, 2013

### collinsmark

The Wikipedia article on signed numbers has some pretty good information about these number systems that you might want to look over.
http://en.wikipedia.org/wiki/Signed_number_representations

For B), are you sure you mean "excess 128 2's complement representation"?

I think the representation can be in "excess 128," or "2's complement" representation, but not both.

I'm not following what you are doing here. Why did you subtract the 1?

Before getting into Excess-128, let's discuss the more general Excess-K as described in the link above.

Excess-K interpretation = Unsigned interpretation - K
(Simply subtract K from the unsigned interpretation.)

For example,
Excess-K interpretation of "0000 0000" is (0 - K) = -K
Excess-K interpretation of "0000 0001" is (1 - K) = -K + 1
Excess-K interpretation of "0000 0010" is (2 - K) = -K + 2
.
.
.
Excess-K interpretation of "1000 0000" is (128 - K) = -K + 128
.
.
.
Excess-K interpretation of "1111 1111" is (255 - K) = -K + 255.

Now let's put some numbers in knowing that K = 128 for this problem.

Excess-K interpretation of "0000 0000" is (0 - 128) = -128
Excess-K interpretation of "0000 0001" is (1 - 128) = -127
...
Excess-K interpretation of "1000 0000" is (128 - 128) = 0
...
Excess-K interpretation of "1111 1111" is (255 - 128) = 127

Does that make sense?

Yes, that's correct for "2's Complement representation."

(But I still don't know what is meant by "excess 128 2's complement representation.")

That doesn't look right for excess 128 representation. See above in part A where I showed some examples.