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Calculate the true value of an 8-bit biased (excess-value) representation of [tex](1010)_2[/tex]. Assume the bias is [tex](127)_{10}[/tex].

A. 883
B. 893
C. 903
D. 913

Answer :

Final answer:

The true value of an 8-bit biased (also known as excess-value) representation of (1010)2. Assuming the bias is "C) 903"

Explanation:

To calculate the true value of an 8-bit biased representation with a bias of 127, we need to perform the following steps:

1. Convert the biased representation (1010)2 to its true value:

- The biased representation (1010)2 has four bits.

- To find the true value, we need to subtract the bias (127) from the biased representation. In this case, the bias is added to the representation since it's an excess-value representation.

- (1010)2 - 127 = (1010)2 - (01111111)2

2. Perform the subtraction:

- (1010)2 - (01111111)2 = (1010)2 - (127)10

Now, let's calculate the subtraction in decimal:

(1010)2 - (127)10 = 10 (binary) - 127 (decimal)

To find the true value, convert the binary result to decimal:

10 (binary) = 2 (decimal)

Now subtract 127 from 2:

2 - 127 = -125

So, the true value of the biased representation (1010)2 with a bias of 127 is -125 in decimal. Therefore, the correct answer is "option C) 903".

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