ALU Instructions

Key Concepts

The LC-3 ALU is a very simple unit with three (3) instructions As a teaching ISA, the LC-3 has limited capabilities. Modern ALUs are capable of 50 or more instructions AND and ADD instruction have two (2) different modes The instruction process 2 16-bit values, but can also process a 16-bit value and a hard-coded value. This second mode is convenient for simple instruction like subtracting 1 from a stored value

Terms

Term	Meaning
ALU	The arithmetic and logic unit (ALU) is a component in the CPU that preforms mathematic and logical functions.
Branching	A technique that causes a program to change the flow of its execution; e.g., if/else and calling a function.
Clock Cycle	A single time segment, controlled by the computer's clock, in which circuits receive input values, process the inputs, and then produce an output.
Condition Code (CC)	Information about the previous instruction's result. Can indicate that the previous instruction resulted in an error/exception, overflow/underflow, or positive/zero/negative value
FDE Cycle	The Fetch-Decode-Execute pattern used by the CPU to execute a single instruction.
Instruction	Single executable line of code in a program. Contains OpCode and Operands.
ISA	Instruction Set Architecture. LIst of all Instruction OpCode and expected Operands.
Memory	Storage used by the program to save and retrieve data. This storage is external to the CPU.
OpCode	Assembly instruction keyword as defined by the ISA.
Operand(s)	Assembly instruction parameters, as defined by the ISA.
Register	Storage used by the CPU to save and retrieve data. These devices directly connected to the CPU's control device and the ALU.
Subroutines	Subset of branching that has added capabilities like passing parameters, throwing exceptions, and returning results.
TRAP Routines	Functions that are built-in to the programming language; e.g., System.out.println() in Java.

Introductions

The LC-3 ALU is capable of executing three (3) operations: ADD, AND, and NOT. Although limited, when combined, these three (3) operations can be used to do many more things that add and compare.

In this section we will review the ALU instructions, options for each, and look at some simple example code.

ADD

LC-3 ISA Format

ADD (Immediate Mode)

OpCode	DR	SR1	Mode	IMM5
0001	000	000	1	00000

OPCode :

DR : Destination Register

SR1 : Source Register 1

Mode : 1 indicates Register Mode

IMM5 : 5-bit immediate value

Examples:

ADD R3, R1, #1 ; Add values in register 1 with 1, store result in R3

ADD R3, R2, #-4 ; Add values in register 2 with -4, store result in R3

ADD R3, R3, xB ; Add value in R3 to hex value B, store result in R3

ADD R3, R3, b0111 ; Add value in R3 to binary value 7, store result in R3

ADD (Register Mode)

OpCode	DR	SR1	Mode	unused	SR2
0001	000	000	0	00	000

OPCode :

DR : Destination Register

SR1 : Source Register 1

Mode : 0 indicates Register Mode

unused : not used in Register Mode

SR2 : Source Register 2

Examples:

ADD R3, R1, R2 ; sum values in registers 1 and 2, store result in R3

ADD R3, R2, R2 ; Add R2 to itself, store result in R3

ADD R3, R3, R3 ; Add value in R3 to itself, store result in R3

Explanation

ADD is the only arithmetic operation in the LC-3 ISA. This command adds 2 16-bit, 2's complement values. The result is stored in a register

The Condition Code (CC) register is updated based on the resulting addition

ADD has 2 modes:

• Register Mode: Add values from 2 register
• Immediate Mode: Add value in 1 register with a hard coded immediate value
  • Immediate value is represented in 5-bits
  • Immediate value is a 2's complement
    • -16 to +15

Examples

General Syntax

ADD DR, SR1, SR2

• DR - Destination Register for resulting operation
• SR1 and SR2 - Source registers for the operation

ADD DR, SR1, Imm5

• DR - Destination Register for resulting operation
• SR1 - Source register for the operation
• Imm5 - 5-bit 2's complement value to add to SR1

Add registers and store in a different register

ADD R0, R1, R2

Add the values in R1 and R2. Store in R0

ADD R0, R1, #6

Add the value in R1 and 6. Store in R0

Add registers and store in a one of the same registers

ADD R1, R1, R2

Add the values in R1 and R2. Store in R1, overwriting the original value in R1

ADD R1, R1, #-3

Add the value in R1 and -3. Store in R1, overwriting the original value in R1

Add a register to itself and store in a different register

ADD R0, R1, R1

Add the values in R1 to itself (double the original value). Store in R0

Add a register to itself and store in the same registers

ADD R1, R1, R1

Add the values in R1 to itself (double the original value). Store in R1, overwriting the original value in R1

Gotchas

• Immediate Value mode can only add a register value and a small number (-16 to +15). To add larger values, use Register mode
• ADD and AND are easy to mix up when typing source code. Double check when you type these instructions. If your program behaves unexpectedly around and ADD instruction, check that you didn't accidentally type AND

AND

LC-3 ISA Format

AND (Immediate Mode)

OpCode	DR	SR1	Mode	IMM5
0101	000	000	1	00000

OPCode :

DR : Destination Register

SR1 : Source Register 1

Mode : 1 indicates Register Mode

IMM5 : 5-bit immediate value

Examples:

AND R3, R1, #1 ; And values in register 1 with 1, store result in R3

AND R3, R2, #-4 ; And values in register 2 with -4, store result in R3

AND R3, R3, xB ; And value in R3 to hex value B, store result in R3

AND R3, R3, b0111 ; Add value in R3 to binary value 7, store result in R3

AND (Register Mode)

OpCode	DR	SR1	Mode	unused	SR2
0101	000	000	0	00	000

OPCode :

DR : Destination Register

SR1 : Source Register 1

Mode : 0 indicates Register Mode

unused : not used in Register Mode

SR2 : Source Register 2

Examples:

AND R3, R1, R2 ; And values in registers 1 and 2, store result in R3

AND R3, R2, R2 ; And R2 to itself, store result in R3

AND R3, R3, R3 ; And value in R3 to itself, store result in R3

Explanation

AND is one of two logic operations in the LC-3 ISA. This command bitwise ands 2 16-bit values. The result is stored in a register

The Condition Code (CC) register is updated based on the resulting and operation.

AND has 2 modes:

• Register Mode: And values from 2 register
• Immediate Mode: And value in 1 register with a hard coded immediate value
  • Immediate value is represented in 5-bits
    • -16 to +15

Examples

AND DR, SR1, SR2

• DR - Destination Register for resulting operation
• SR1 and SR2 - Source registers for the operation

AND DR, SR1, Imm5

• DR - Destination Register for resulting operation
• SR1 - Source register for the operation
• Imm5 - 5-bit 2's complement value to AND to SR1

AND registers and store in a different register

AND R0, R1, R2

And the values in R1 and R2. Store in R0

AND R0, R1, #6

And the value in R1 and 6. Store in R0

AND registers and store in a one of the same registers

AND R1, R1, R2

And the values in R1 and R2. Store in R1, overwriting the original value in R1

AND R1, R1, #-3

And the value in R1 and -3. Store in R1, overwriting the original value in R1

AND a register to itself and store in a different register

AND R0, R1, R1

And the values in R1 to itself (double the original value). Store in R0

AND a register to itself and store in the same registers

AND R1, R1, R1

And the values in R1 to itself (double the original value). Store in R1, overwriting the original value in R1

Gotchas

• Immediate Value mode can only add a register value and a small number (-16 to +15). To add larger values, use Register mode
• The Immediate Value will be sign-extended, Remember that the most significant bits [15-5] will be all zeros (0) or ones (1) based on the sign
• ADD and AND are easy to mix up when typing source code. Double check when you type these instructions. If your program behaves unexpectedly around and AND instruction, check that you didn't accidentally type ADD

NOT

LC-3 ISA Format

NOT

OpCode	DR	SR	unused
1001	000	000	000000

OPCode :

DR : Destination Register

SR1 : Source Register

unused : not used in Register Mode

Examples:

NOT R3, R3 ; Not value in R3, store result in R3

NOT R3, R2 ; Not value in R2, store result in R3

Explanation

NOT is the other logic operations in the LC-3 ISA. This command bitwise nots a 16-bit value. The result is stored in a register

The Condition Code (CC) register is updated based on the resulting negation.

Examples

NOT DR, SR

• DR - Destination Register for resulting operation
• SR - Source register for the operation

NOT register and store in a different register

NOT R0, R1

Not the value in R1. Store in R0

NOT register and store in the same register

NOT R1, R1

Not the value in R1. Store in R0, overwriting the original value in R1

Gotchas

The LC-3 Simulate tool shows Hex and Decimal values of 16-bit data stored in Memory and Registers. Simulate does this 'to be helpful' to the developer. When storing data for logical operations, it falls to the developer to remember that the bits are representing bits.

Conclusion

The LC-3 Arithmetic Logic Unit (ALU) is capable of performing one (1) arithmetic instruction, ADD, and two (2) logic functions (AND, NOT).

ADD and AND have two (2) modes that define the input data elements to use. Register mode pulls data from two (2) registers. Immediate mode pulls data from one (1) register and a hard-coded value that is defined in the instruction.

Once the CPU Controller has all the information to complete an ALU instruction, it send the data and operation to the ALU to complete. Results are send back to the Controller to store.