Final answer:
To test for overflow in MIPS, 'add' instruction uses sign comparison for signed addition, while 'addu' checks for a carry out in unsigned addition. Both utilize the ALU to detect an overflow condition and set a flag that the control unit can check for possible exceptions.
Step-by-step explanation:
The hardware for testing overflow in the MIPS architecture during signed and unsigned addition can be described by understanding how overflow is detected. In the MIPS instruction set, the 'add' instruction is used for signed addition, while the 'addu' instruction is for unsigned addition.
Detecting overflow for signed addition involves checking the sign of the two operands. If the signs are the same, then an overflow has occurred if the sign of the result differs from the operands. Here's a simple module diagram perspective:
- Add the two operand values together.
- Check if both operands are positive or both operands are negative(using the most significant bit, MSB, as the sign bit).
- If so, check the MSB of the result. If it differs from the operands' MSB, an overflow has occurred.
For the unsigned 'addu' instruction, overflow occurs if there is a carry out of the most significant bit because unsigned numbers are always positive, and any carry out would indicate that the result cannot be represented in the fixed number of bits.
- Perform the addition of the two operand values.
- Examine the carry out of the most significant bit.
- If there is a carry out, an overflow has occurred.
Hardware implementations use an arithmetic logic unit (ALU) that indeed has the capability to detect these conditions and set an overflow flag accordingly during the operation. This flag can then be checked by the control unit to determine if an overflow exception needs to be raised.