Can help me with mips translating to binary?

Question

I don't understand how to translate a label. Anyone can give me a help

suppose we have the following code:

loop: 
    add $t2,$t2,$t1 
    addi $t2,$t2,4 
    sw $t2,4($s0) 
    bne $t2,20,loop 
    jr $ra

How translate to binary bne $t2,10,loop ?

Answer 1

A few things to note.

The branch offset is always calculated from the address of the branch + 4 (i.e. PC+4), so it is relative to the address of the jr instruction.

Since mips instructions must be aligned to a word [four byte boundary], the rightmost two bits of an instruction address will be [must always be] zero.

The mips architecture takes advantage of that by encoding a branch offset as a word offset (i.e. the byte offset is shifted right by 2). This extends the range of a branch instruction 16 bit immediate encoding to 18 bits.

So, here is the listing:

00:     loop:
00:         add     $t2,$t2,$t1
04:         addi    $t2,$t2,4
08:         sw      $t2,4($s0)
0C:         bne     $t2,20,loop
10:         jr      $ra

The jr address is 0x10, so the byte offset for loop would be -0x10 and the encoded offset would be -0x04 or 0xFFFC and the bne would be xxxxFFFC

But ... There is a problem with that. This particular bne uses an immediate value for the second argument. This makes the bne a pseudo-op and not a simple bne instruction.

So, the actual sequence becomes:

00:     loop:
00:         add     $t2,$t2,$t1
04:         addi    $t2,$t2,4
08:         sw      $t2,4($s0)
0C:         addi    $at,$zero,20
10:         bne     $at,$t2,loop
14:         jr      $ra

Note that the bne becomes a two instruction sequence: addi and bne

The jr address is now 0x14, so the byte offset for loop would be -0x14 and the encoded offset would be -0x05 or 0xFFFB and the bne would be xxxxFFFB

The bne assembler format is:

    bne    s,t,label

The bne encoding is:

0001 01ss ssst tttt iiii iiii iiii iiii

So, the s register is $at or $1 --> 00001

The t register is $t2 or $10 --> 01010

So, now we have:

0001 01ss ssst tttt iiii iiii iiii iiii
       00 0010 1010
0001 0100 0010 1010 iiii iiii iiii iiii

In hex, this is 142Ayyyy. We already know that yyyy is FFFB, so the final hex value is: 142AFFFB