Designing a microprogrammed control circuit for the addition and subtraction of binary numbers in sign-magnitude form involves creating a control unit that generates microinstructions to control the data path and operations required for addition and subtraction. The control unit uses microcode to implement the desired behavior of the processor for these operations. Below are the steps to design such a microprogrammed control circuit:
Step 1: Define Microinstructions and Control Signals Define the microinstructions required to perform the addition and subtraction operations. Each microinstruction represents a specific control action to be taken by the processor during the execution of the operation. Determine the control signals needed to control the various components in the data path, such as the ALU, registers, and flags.
Step 2: Create Microinstruction Format Design the format of each microinstruction, specifying the fields for the control signals, registers, and other relevant information. The format should be able to accommodate all the control signals required for addition and subtraction.
Step 3: Develop Microcode Sequences for Addition Write the microcode sequences for addition in sign-magnitude form. The microcode sequences should include steps to perform sign extension, addition of the magnitudes, handling of sign bits, and setting the appropriate flags (e.g., carry, overflow).
Step 4: Develop Microcode Sequences for Subtraction Write the microcode sequences for subtraction in sign-magnitude form. The microcode sequences should include steps to perform sign extension, two’s complement conversion of the subtrahend, addition of the magnitudes (using the ALU), handling of sign bits, and setting the appropriate flags (e.g., carry, overflow).
Step 5: Implement Control Logic Create the control logic that interprets the microinstructions and generates the corresponding control signals for each operation. The control logic is responsible for decoding the microinstruction format, fetching the appropriate control signals, and coordinating the execution of the addition and subtraction operations.
Step 6: Microprogram Sequencer Design the microprogram sequencer, which is responsible for sequencing through the microinstructions during the execution of addition and subtraction operations. It generates the microinstruction addresses and provides control for branching and looping within the microcode sequences.
Step 7: Implement Data Path Design the data path, including registers, ALU, and other necessary components to support the addition and subtraction operations. The data path should be able to handle the input operands, perform arithmetic operations, and store the results.
Step 8: Testing and Verification Thoroughly test the microprogrammed control circuit with various test cases for addition and subtraction in sign-magnitude form. Verify that the control signals and data path operations are correctly executed and that the results are accurate.
Step 9: Optimization (Optional) Optimize the microcode to improve performance and reduce the number of microinstructions. This step may involve techniques such as loop unrolling, common subexpression elimination, and minimizing unnecessary control signal transitions.
Step 10: Integration Integrate the microprogrammed control circuit with the rest of the processor architecture to create a complete microprocessor capable of performing addition and subtraction in sign-magnitude form.
