Opcode 000 001 010 011 100 101 110 111 Operation O=B O=A^B (bitwise xor) O=A AND B (bitwise and) O=A OR B (bitwise or) O= A + B (addition) O=A - B (subtract) O(7) = 0, 0(6:0) = B (7:1) (logical shift right) O=AB (multiplication) Description Output is equal to input B E Xor of each bit in A with the corresponding bit in B AND of each bit in A with the corresponding bit in B OR of each bit in A with the corresponding bit in B 8 bit addition with a final carry out bit 8 bit subtraction with a borrow out bit Logical shift of the data at input B right by one bit 8 Multiplication. To make our design simpler, we will only keep the lower 8 bits of the result and signal an overflow

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Can you help make a Boolean algebra equation or truth table of the results and simplify it with a k-map for the multiplication part please?
### Opcode Table for Logical and Arithmetic Operations

Here is a detailed explanation of operations performed by various opcodes, specifically for educational purposes in digital logic design.

| **Opcode** | **Operation**              | **Description**                                                                 |
|------------|----------------------------|---------------------------------------------------------------------------------|
| 000        | O = B                      | Output is equal to input B.                                                     |
| 001        | O = A ^ B (bitwise XOR)    | XOR of each bit in A with the corresponding bit in B.                           |
| 010        | O = A AND B (bitwise AND)  | AND of each bit in A with the corresponding bit in B.                           |
| 011        | O = A OR B (bitwise OR)    | OR of each bit in A with the corresponding bit in B.                            |
| 100        | O = A + B (addition)       | 8-bit addition with a final carry out bit.                                      |
| 101        | O = A - B (subtraction)    | 8-bit subtraction with a borrow out bit.                                        |
| 110        | O(7) = 0, O(6:0) = B(7:1)  | Logical shift of the data at input B right by one bit.                          |
| 111        | O = A * B (multiplication) | 8-bit multiplication. Only the lower 8 bits of the result are kept, with overflow signaled. |

### Explanation of Operations:

- **Bitwise Operations (XOR, AND, OR):**
  - Bitwise operations are performed between corresponding bits of inputs A and B, resulting in output O.

- **Arithmetic Operations (Addition, Subtraction, Multiplication):**
  - These operations handle standard arithmetic between binary values with attention to carry and overflow.

- **Logical Shift:**
  - The logical shift operation moves bits to the right, filling the vacant positions with zeros, effectively dividing the number by 2.

This table serves as a foundation for understanding basic binary operations in digital systems.
Transcribed Image Text:### Opcode Table for Logical and Arithmetic Operations Here is a detailed explanation of operations performed by various opcodes, specifically for educational purposes in digital logic design. | **Opcode** | **Operation** | **Description** | |------------|----------------------------|---------------------------------------------------------------------------------| | 000 | O = B | Output is equal to input B. | | 001 | O = A ^ B (bitwise XOR) | XOR of each bit in A with the corresponding bit in B. | | 010 | O = A AND B (bitwise AND) | AND of each bit in A with the corresponding bit in B. | | 011 | O = A OR B (bitwise OR) | OR of each bit in A with the corresponding bit in B. | | 100 | O = A + B (addition) | 8-bit addition with a final carry out bit. | | 101 | O = A - B (subtraction) | 8-bit subtraction with a borrow out bit. | | 110 | O(7) = 0, O(6:0) = B(7:1) | Logical shift of the data at input B right by one bit. | | 111 | O = A * B (multiplication) | 8-bit multiplication. Only the lower 8 bits of the result are kept, with overflow signaled. | ### Explanation of Operations: - **Bitwise Operations (XOR, AND, OR):** - Bitwise operations are performed between corresponding bits of inputs A and B, resulting in output O. - **Arithmetic Operations (Addition, Subtraction, Multiplication):** - These operations handle standard arithmetic between binary values with attention to carry and overflow. - **Logical Shift:** - The logical shift operation moves bits to the right, filling the vacant positions with zeros, effectively dividing the number by 2. This table serves as a foundation for understanding basic binary operations in digital systems.
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