The problem asks to find the denary (decimal) representation of the 8-bit signed binary number $10001101$. We need to consider that the number is a signed number, which most likely means it is represented using two's complement. Also, we need to comment on the validity of the result.

1. Problem Description

The problem asks to find the denary (decimal) representation of the 8-bit signed binary number $10001101$. We need to consider that the number is a signed number, which most likely means it is represented using two's complement. Also, we need to comment on the validity of the result.

2. Solution Steps

Since the number is given as an 8-bit signed number, we can assume two's complement representation.

The given binary number is $10001101$.

* Step 1: Check the most significant bit (MSB). If the MSB is 0, the number is positive. If the MSB is 1, the number is negative.

In this case, the MSB is 1, so the number is negative.

* Step 2: Find the two's complement of the number. To find the two's complement, we first invert the bits (change 0s to 1s and 1s to 0s), and then add

1. Inverting the bits of $10001101$ gives $01110010$.

Adding 1 to $01110010$ gives $01110011$.

* Step 3: Convert the two's complement to decimal.

$01110011_2 = 0 \cdot 2^7 + 1 \cdot 2^6 + 1 \cdot 2^5 + 1 \cdot 2^4 + 0 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0$

$= 0 + 64 + 32 + 16 + 0 + 0 + 2 + 1 = 115_{10}$

* Step 4: Since the original number was negative, the decimal representation is the negative of the two's complement's decimal value.

Therefore, the denary representation of $10001101$ is $-115$.

* Step 5: Check validity

For 8-bit two's complement, the range is $-2^{7}$ to $2^{7}-1$, which means -128 to

1

2

7. Since $-128 \le -115 \le 127$, the result is valid.

3. Final Answer

The denary representation of the 8-bit signed binary number $10001101$ is $-115$. The result is valid.