what would be the encoding of a bnez MIPS instruction?

Question

What would be the encoding of this last instruction if the address of the Loop is 0x00012344?

Loop:
    addu $a0, $0, $t0
    ori $v0, $0, 4
    syscall
    addi $t0, $t0, -1
    bnez $t0, Loop

this last instruction is equivalent to:

bne $t0, $0, Loop

however, How would I write this in machine code?

this is how for I got:

000101 01000 00000 iiiii iiiii iiiiii

I dont know what to but for the i's here. The address of Loop is 0x00012344 however that is a 17 bit binary number. I only have 16 bits

Answer 1

Branch in MIPS works with offsets (shifted left 2 positions), not absolute addresses.

BNE -- Branch on not equal

Description:

Branches if the two registers are not equal

Operation:

if $s != $t advance_pc (offset << 2)); else advance_pc (4);

Syntax:

bne $s, $t, offset

Encoding:

0001 01ss ssst tttt iiii iiii iiii iiii

Source

So it's Loop offset from the BNE instruction that should go on the i part, not its absolute address.

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EDIT: with edited question code:

Loop:
    addu $a0, $0, $t0
    ori $v0, $0, 4
    syscall
    addi $t0, $t0, -1
    bnez $t0, Loop

Since all MIPS instructions are 32-bit wide (4 bytes), we can calculate offset easily:

• Loop address is -4 instructions from BNEZ instruction, so it's -4 x 4 = -16 bytes away.
• But we need to add one more word because in MIPS PC was already incremented by 4 and when BNEZ is executing, PC is already pointing to next instruction (see delay slot in MIPS). So final offset is -20 = -(0x14) = 0xFFFEC.
• We shift right 2 positions (divide by 4) to get this offset in words (instead of bytes): 0xFFFEC >> 2 = 0xFFFB

You can also do it by counting by words directly:

• Loop address is -4 instructions from BNEZ instruction
• Additional -1 because PC already incremented: -5
• -5 = -(0x5) = 0xFFFB

So we got 0xFFFB for i part; so whole instruction is 0x1500FFFB.

By the way you can check this with any MIPS assembler or simulator.

(Screenshot from MARS simulator)