Refined bitwise division algorithm in MIPS - algorithm

Question

Our assignment is to implement a refined bitwise division algorithm in MIPS.
Basically in the refined program, we load the dividend into the LO bits of the 64 bit register and the remainder will accumulate in the HI bits, which are originally all set to 0.
Then we simply test if HI (our remainder) > = divisor.
If our accumulating remainder is not currently > = divisor, we simply left shift the entire register and fill in with a 0. This is the beginning of our quotient. As the dividend bits move into HI, we will finally have a situation where HI > =
divisor. Then we will subtract the divisor from HI, shift the entire register left, and fill in with a 1.
In short, we can simply continue to shift all 64 bits left, filling in with a 0 when HI < divisor, subtracting the divisor from HI and filling in with a 1 when HI > = divisor.
In our homework, we are to write a program to accept two positive numbers (16 bit signed numbers) from the console, divide the former by the latter.
I put the divisor in $t0, the remainder in $t3, and the dividend in $t2. $t3 and $t2 are both 16 bits, and together they pair up to be a 32-bit register. Somehow, my program returns a really funky quotient: the least significant few bits are correct, but the most significant is always 1; somehow I can't get rid of the 1, no matter how many bits I shift left. For instance, if the dividend is 1000, by shifting left, instead of getting 0001 0000, I actually get 10000 - MSB is always 1. Could someone please take a look at my program and give me some suggestions? Thanks a lot!
.data
GETA: .asciiz "Enter Dividend: "
GETB: .asciiz "Enter Divisor: "
QT: .asciiz "Quotient = "
RM: .asciiz "Remainder = "
NL: .asciiz "\n"
.text
main:
li $v0, 4 #Prompt for a dividend
la $a0, GETA
syscall
li $v0, 5 #Read dividend from user
syscall
move $t2, $v0 #dividend in $t2
li $v0, 4 #Prompt for a divisor
la $a0, GETB
syscall
li $v0, 5 #Read divisor from user
syscall
move $t0, $v0 #divisor in $t0
addi $t4, $zero, 17 #counter
j Loop
Loop:
slt $t1, $t3, $t0 #if remainder < divisor, $t1=1
beq $t1, $zero, subroutine #remainder >= divisor, $t1=0
#if remainder < divisor
sll $t3, $t3, 1 #shift remainder by to left by 1
andi $t5, $t2, 32768 #get MSB of $t2
bne $zero, $t5, updateRemainder1 #MSB of $t2 is 1
#MSB of $t2 is 0
sll $t2, $t2, 1 #shift dividend to left by 1
addi $t4, $t4, -1 #decrease counter by 1
bne $zero, $t4, Loop
j Exit
subroutine:
sub $t3, $t3, $t0 #subtract divisor from remainder
sll $t3, $t3, 1 #shift remainder by to left by 1
andi $t5, $t2, 32768 #get MSB of $t2
bne $zero, $t5, updateRemainder2 #MSB of $t2 is 1
#MSB of $t2 is 0
sll $t2, $t2, 1 #shift dividend to left by 1
ori $t2, $t2, 1 #fill in LSB of $t2 with a 1
addi $t4, $t4, -1 #decrease counter by 1
bne $zero, $t4, Loop
j Exit
updateRemainder1:
ori $t3, $t3, 1 #set LSB of remainder to 1
sll $t2, $t2, 1 #shift dividend to left by 1
addi $t4, $t4, -1 #decrease counter by 1
bne $zero, $t4, Loop
j Exit
updateRemainder2:
ori $t3, $t3, 1 #set LSB of remainder to 1
sll $t2, $t2, 1 #shift dividend to left by 1
ori $t2, $t2, 1 #fill in LSB of $t2 with a 1
addi $t4, $t4, -1 #decrease counter by 1
bne $zero, $t4, Loop
j Exit
Exit:
sub $t2, $t2, 524288
li $v0, 4 #print out output line
la $a0, QT
syscall
li $v0, 1 #print out quotient
move $a0, $t2
syscall
li $v0, 4 #print out new line
la $a0, NL
syscall
li $v0, 4 #print out output line
la $a0, RM
syscall
li $v0, 1 #print out remainder
move $a0, $t3
syscall
li $v0, 10
syscall