3. Let LSA(x,b) represent a left arithmetic shift of x by b bits, and RSL(x,b) represent a right logical shift of x by b bits. Using two's complement binary with fixed size of 16 bit, what is the result (in decimal) of the expression LSA(-1610,8) + RSL(-12810,4)? A) 110 XB) -810 C) -11210 D) -66₁10 E) -12810 F) -17210

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**Problem 3:**

**Description:** 

Let LSA(x, b) represent a left arithmetic shift of x by b bits, and RSL(x, b) represent a right logical shift of x by b bits. Using two’s complement binary with a fixed size of 16 bits, determine the resulting decimal value of the following expression:

\[ \text{LSA}(-16_{10}, 8) + \text{RSL}(-128_{10}, 4) \]

**Options:**

A) \( 1_{10} \) 

B) \(-8_{10}\) 

C) \(-112_{10}\) 

D) \(-66_{10}\) 

E) \(-128_{10}\) 

F) \(-172_{10}\) 

**Explanation:**

- **Left Arithmetic Shift (LSA):** Moves all bits to the left by a specified number of positions (b), while preserving the sign bit for the most significant bit.

- **Right Logical Shift (RSL):** Moves all bits to the right by a specified number of positions (b) while filling the vacated bit positions with zeros, regardless of the sign bit.

**Objective:**

Calculate the value in decimal for \( \text{LSA}(-16_{10}, 8) + \text{RSL}(-128_{10}, 4) \) using 16-bit two’s complement representation.
Transcribed Image Text:**Problem 3:** **Description:** Let LSA(x, b) represent a left arithmetic shift of x by b bits, and RSL(x, b) represent a right logical shift of x by b bits. Using two’s complement binary with a fixed size of 16 bits, determine the resulting decimal value of the following expression: \[ \text{LSA}(-16_{10}, 8) + \text{RSL}(-128_{10}, 4) \] **Options:** A) \( 1_{10} \) B) \(-8_{10}\) C) \(-112_{10}\) D) \(-66_{10}\) E) \(-128_{10}\) F) \(-172_{10}\) **Explanation:** - **Left Arithmetic Shift (LSA):** Moves all bits to the left by a specified number of positions (b), while preserving the sign bit for the most significant bit. - **Right Logical Shift (RSL):** Moves all bits to the right by a specified number of positions (b) while filling the vacated bit positions with zeros, regardless of the sign bit. **Objective:** Calculate the value in decimal for \( \text{LSA}(-16_{10}, 8) + \text{RSL}(-128_{10}, 4) \) using 16-bit two’s complement representation.
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