Summary Checklist

Bit Arrangement

R-FormatI-FormatJ-Format

`opcode`	`$rs`	`$rt`	`$rd`	`shamt`	`funct`
6	5	5	5	5	6

`opcode`	`$rs`	`$rt`	`immediate`
6	5	5	16

`opcode`	`immediate`
6	26

The full comparison where the bits are aligned is shown below. The number of bits is shown inside a square bracket.

Format	Fields
R-Format	`opcode` [6]	`$rs` [5]	`$rt` [5]	`$rd` [5]	`shamt` [5]	`funct` [6]
I-Format	`opcode` [6]	`$rs` [5]	`$rt` [5]	`immediate` [16]
J-Format	`opcode` [6]	`immediate` [26]

or to put it in picture:

Bit Arrangement

Note

Branches and load/store are both I-format instructions.
- Branches use PC-relative addressing.
- Load/store use base addressing.
Shifts use R-format but other immediate instructions (i.e., addi, andi, ori, slti) use I-format.
J-format use pseudo-direct addressing.
- Compared to branches which use PC-relative addressing.

Opcode/Funct Values

Funct Values

Operation	Hexadecimal	Decimal
`add`	20	32
`sub`	22	34
`sll`	00	00
`srl`	02	02
`and`	24	36
`or`	25	37
`xor`	26	38
`nor`	27	39

Opcode Values

Operation	Hexadecimal	Decimal
R-Format	00	00
`j`	02	02
`beq`	04	04
`bne`	05	05
`addi`	08	08
`andi`	0C	12
`ori`	0D	13
`xori`	0E	14
`lb`	20	32
`lw`	23	35
`sb`	28	40
`sw`	2B	43

Immediate Field

Branch

Branch Calculation

If the branch is not taken:

$PC' = $PC + 4
If the branch is taken:

$PC' = ($PC + 4) + (immediate × 4)

Here, $PC + 4 is the address of the next instruction and $PC' is the target address. Why do we use $PC + 4 when the branch is not taken? The reason will be clearer when we show the processor implementation.

The advantage of this computation is that the immediate value specifies the number of instruction to "skip over" (from the next instruction).

Quick Branch Calculation

The immediate value specifies the number of instruction to "skip over" (from the next instruction).

Draw a line below the current instruction (this represents the $PC + 4).
Draw a line above the target instruction (this represents the $PC').
Complete the box.
Count the number of instructions within the box (this represents the immediate × 4).
- If the target label is after, keep the value as positive.
- If the target label is before, convert the value to negative.

Jump

Address Calculation

Without bitwise operations:

$PC' = ($PC + 4) - (($PC + 4) % 268435456) + (immediate × 4)
With bitwise operations:

$PC' = (($PC + 4) & 0xF0000000) | (immediate × 4)

Here, $PC + 4 is the address of the next instruction and $PC' is the target address. 268435456 is equal to 2²⁸. Now, calculating the address is probably more difficult due to the magic number. So, we will also illustrate it with a diagram below.

Address Calculation

Summary Table

The following summary shows only selective instructions. Hopefully you can extrapolate this to other instructions of similar kinds.

Do NOT Sort

There is a bug in the table sorting mechanism due to some cell spanning multiple rows. If you accidentally sort the table, simply reload the page.

Category	Instruction	Example	Meaning	Comments
Arithmetic	Addition	`add $rd, $rs, $rt`	`$rd = $rs + $rt`	3 operands; register addressing
	Subtraction	`sub $rd, $rs, $rt`	`$rd = $rs - $rt`	3 operands; register addressing
	Add Immediate	`addi $rt, $rs, imm`	`$rt = $rs + imm`	Used to add constants
Data Transfer	Load Word	`lw $rt, offset($rs)`	`$rt = MEM[$rs + offset]`	Word from memory to register
	Store Word	`sw $rt, offset($rs)`	`MEM[$rs + offset] = $rt`	Word from register to memory
	Load Byte	`lb $rt, offset($rs)`	`$rt = MEM[$rs + offset]`	Byte from memory to register
	Store Byte	`sb $rt, offset($rs)`	`MEM[$rs + offset] = $rt`	Byte from register to memory
	Load Upper Immediate	`lui $rt, imm`	`$rt = imm << 16` or `$rt = imm × 2¹⁶`	Load cosntant in upper 16 bits
Branch	Branch on Equal	`beq $rs, $rt, imm`	`$PC = ($rs == $rt) ? ($PC+4)+(imm×4) : ($PC+4)`	Equal test; PC-relative branch
	Branch on Not Equal	`bne $rs, $rt, imm`	`$PC = ($rs != $rt) ? ($PC+4)+(imm×4) : ($PC+4)`	Not equal test; PC-relative branch
	Set on Less Than	`slt $rd, $rs, $rt`	`$rd = ($rs < $rt) ? 1 : 0`	Compare less than; for `beq` or `bne`
	Set on Less Than Immediate	`slti $rt, $rs, imm`	`$rt = ($rs < imm) ? 1 : 0`	Compare less than constant; for `beq` or `bne`
Jump	Jump	`j imm`	`$PC = (($PC+4) & 0xF0000000) \| (imm×4))`	Jump to target address; pseudo-direct addressing
	Jump Register	`jr $ra`	`$PC = $ra`	For switch, procedure return
	Jump and Link	`jal imm`	`$ra = $PC+4` then `$PC = (($PC+4) & 0xF0000000) \| (imm×4))`	For procedure call

MIPS Assembler

We have a MIPS assembler that admits the same MIPS syntax as MIPS interpreter. To correctly assemble j instruction, you will need to specify the base address (i.e., the address of the first instruction of the program). This base address will need to be word-aligned (i.e., multiple of 4). If none is specified, it will be assumed to be 0. Note that the base address should be specified as hexadecimal without the prefix 0x.

Currently, the assembler assumes that the code can be assembled correctly. As such, it does not check if there is a jump at the boundary.