# Arithmetic Instructions Computers are constantly performing calculations. Adding numbers, subtracting values, increasing counters, and comparing numerical quantities are all common operations performed by a processor. The CPU performs these operations using arithmetic instructions. Arithmetic instructions are a type of data manipulation instruction because they operate on and produce data values. What Are Arithmetic Instructions? Arithmetic instructions are instructions that perform mathematical operations on data. Common arithmetic operations include: Addition Subtraction Multiplication Division Increment Decrement These operations are generally performed by the Arithmetic and Logic Unit (ALU). A simplified view is: Operands ↓ ALU ↓ Arithmetic Result 1. Addition The ADD instruction performs addition. For example: ADD R1, R2 Conceptually: R1 + R2 → Result Depending on the instruction set, the result may replace one operand or be placed in another destination register. For example: R1 = 10 R2 = 5 After an addition: Result = 15 Addition is one of the most fundamental operations performed by a processor. 2. Subtraction The SUB instruction performs subtraction. For example: SUB R1, R2 Conceptually: R1 − R2 → Result If: R1 = 10 R2 = 4 the result is: 6 Subtraction is also commonly used when calculating differences, counters, addresses, and other values. 3. Multiplication The MUL instruction performs multiplication when supported by the processor's instruction set. For example: MUL R1, R2 Conceptually: R1 × R2 → Result If: R1 = 6 R2 = 4 the result is: 24 The hardware implementation of multiplication varies between processor architectures. Some processors have dedicated multiplication hardware, while other designs can perform multiplication through sequences of simpler operations. 4. Division The DIV instruction performs division when supported. For example: DIV R1, R2 Conceptually: R1 ÷ R2 → Result Depending on the architecture, division can produce a quotient and possibly a remainder. For example: 20 ÷ 6 produces: Quotient = 3 Remainder = 2 The exact way these results are stored depends on the instruction set. 5. Increment The increment operation increases a value by one. Conceptually: R1 + 1 → R1 For example: R1 = 7 After incrementing: R1 = 8 An increment instruction is commonly useful for: Counters Loops Addresses Iterating through data A processor may provide a dedicated instruction such as: INC R1 6. Decrement The decrement operation decreases a value by one. Conceptually: R1 − 1 → R1 For example: R1 = 7 After decrementing: R1 = 6 A processor may provide an instruction such as: DEC R1 Decrement operations are commonly used with: Counters Loops Index values Iterative algorithms Arithmetic Instructions and the ALU The Arithmetic and Logic Unit (ALU) is responsible for performing many arithmetic and logical operations inside the CPU. A simplified operation looks like: ```plaintext R1 ─────┐ │ ▼ ┌─────┐ R2 ──►│ ALU │ └──┬──┘ │ ▼ Result ``` The instruction tells the Control Unit which operation should be performed. For example: ADD → perform addition SUB → perform subtraction The Control Unit coordinates the operation, while the ALU performs the actual arithmetic. Arithmetic Instructions and Registers Registers usually provide the operands needed by the ALU. For example: R1 = 15 R2 = 5 An addition operation may conceptually follow: R1 ──┐ ├──► ALU ──► Result R2 ──┘ The result can then be stored in a register. This is why registers and the ALU work closely together. Arithmetic Instructions and Flags Arithmetic operations can affect the processor's status flags. For example, an arithmetic operation may produce: Zero Carry Negative result Overflow Consider: 5 - 5 = 0 The result is zero, so a processor may set its Zero Flag. These flags can later be used by program control instructions to make decisions. For example: Compare values ↓ Set flags ↓ Conditional branch This creates an important connection between arithmetic instructions and program control instructions. Integer Overflow Because registers have a fixed number of bits, they cannot represent unlimited values. For example, an unsigned 8-bit register can represent: 0 to 255 If we try to calculate: 255 + 1 using an 8-bit unsigned representation, the mathematical result is 256, which cannot be represented in 8 bits. The result wraps according to the arithmetic rules of the system, and a carry may be produced. Signed arithmetic also has its own overflow conditions. Understanding overflow becomes especially important when working with low-level programming and assembly language. Example of a Complete Arithmetic Sequence Suppose: R1 = 10 R2 = 5 A simplified sequence could be: ADD R1, R2 Result: 15 Then: INC R1 Result: 16 Then: SUB R1, R2 Result: 11 The processor performs each operation according to the instruction set's rules. Arithmetic vs Data Transfer It is important to distinguish arithmetic instructions from data transfer instructions. Data Transfer Moves data: R1 → R2 Arithmetic Processes data: R1 + R2 A program often needs both. For example: LOAD R1, value ADD R1, R2 STORE R1, result Here: LOAD → transfers data ADD → manipulates data STORE → transfers data Common Arithmetic Instructions Instruction Operation ADD Addition SUB Subtraction MUL Multiplication DIV Division INC Increment by 1 DEC Decrement by 1 The exact instruction names, operands, and behavior depend on the processor architecture. Why Arithmetic Instructions Matter Almost every type of software eventually depends on arithmetic operations. Arithmetic instructions are used in: Calculations Counters Loops Address calculations Algorithms Graphics Scientific computing Operating systems Embedded systems At the hardware level, these operations are reduced to operations that the processor's digital circuits can perform. Final Thoughts Arithmetic instructions allow the CPU to manipulate numerical data. The most common operations are: ADD → Addition SUB → Subtraction MUL → Multiplication DIV → Division INC → Increment DEC → Decrement The ALU performs the arithmetic operation, while registers provide the operands and store results. Arithmetic operations can also affect status flags, which can later influence program control. We've now learned how the processor moves data and how it performs arithmetic on data. But numbers aren't the only thing a CPU needs to manipulate. The processor also needs to work directly with individual bits. Next: Logical Instructions.