# Decimal Values of 8-Bit Bit Patterns

• ccky
In summary, the decimal values for the given 8-bit bit patterns are: A) 126 in excess 128 representationB) -126 in 2's complement representationC) -128 in excess 128 representation

## Homework Statement

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

Binary
2's complement

## 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?

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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

ccky said:

## Homework Statement

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
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.

C)10000010 in excess 128 representation

Binary
2's complement

## The Attempt at a Solution

A(00000010)-1
(00000001)
=11111110.
=254-128=126
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?

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

C)130
Is it right or wrong?
That doesn't look right for excess 128 representation. See above in part A where I showed some examples.

## 1. What are decimal values of 8-bit bit patterns?

The decimal values of 8-bit bit patterns are the numerical representations of binary numbers in base 10. They range from 0 to 255, with each bit representing a power of 2.

## 2. How are decimal values of 8-bit bit patterns calculated?

To calculate the decimal value of an 8-bit bit pattern, each bit is multiplied by its corresponding power of 2 and then added together. For example, the bit pattern 01101101 has a decimal value of (0*2^7) + (1*2^6) + (1*2^5) + (0*2^4) + (1*2^3) + (1*2^2) + (0*2^1) + (1*2^0) = 109.

## 3. What is the maximum decimal value that can be represented by an 8-bit bit pattern?

The maximum decimal value that can be represented by an 8-bit bit pattern is 255. This is because 8 bits can represent 2^8 or 256 different combinations, starting from 0 to 255.

## 4. How are negative decimal values represented in 8-bit bit patterns?

In 8-bit bit patterns, negative decimal values are represented using the two's complement method. This involves flipping all the bits in a number and adding 1 to the result. For example, the 8-bit bit pattern 11111111 represents the decimal value -1 using two's complement.

## 5. Why are 8-bit bit patterns commonly used in computing?

8-bit bit patterns are commonly used in computing because they provide enough combinations to represent a wide range of characters, symbols, and numbers. They are also easy to work with and can be quickly processed by computer hardware.