Is it possible to create a dynamic array in MIPS?

Hi experts,

My homework assignment is to take a number of base 10 from the user and convert it into a base of their choice.    I've been testing my code with just base 2 right now, and I'm suppose to store the intermediate values into an array.  For example:

Take 49 of base 10 and convert it to its equivalent in base 2.  49 = 110001

Since there are a total of 6 digits, I would store it in a .space 24.  But since the number of digits will vary depending on the number the user inputs, I don't know what size of an array to make, so I thought I would try to create, in a sense, a dynamic array.

When I know the size of the array I put
.data
array: .space 24

But, of course, this time I don't know the size.

My homework isn't about arrays, per se.  It's actually about functions, this is just the approach I'm taking.

Since it's getting late here, if I don't respond to your comments this evening I will tomorrow afternoon.

Thank you!

This is the code that I have so far (I hope it and my comments are readable!):

li $v0, 5				# input x
	syscall
	move $t0 $v0				# y = x
	
	li $s1 2				# test instruction
	mul $t1 $s1 2				# A = base times base
	add $t9 $t9 1				# slot counter
bGetSlotLoop:
	add $t1 $t1 $t1				# B = A^N
	add $t9 $t9 1				# slot counter
	ble $t1 $t0 bGetSlotLoop
	
	mul $t3 $t9 4                # arraySize = slot counter * word
	li $v0, 9
	move $a0, $t3
	syscall
	move $s0 $v0
	
	
	li $t1 0
	li $t3 0
bDivBase:
	div $t2 $t0 2		     # newDividend = nextDividend / newBase 
	mflo $t6		     
	mul $t7 $t6 2		     # newProduct = hiQuotient times newBase
	sub $t8 $t0 $t7		     # newNumber = oldDividend - newProduct
	sw $t8 0($t3)		     # newNumber[i] = remainder of quotient
	                             # ///This is where I know my problem is.   
        addi $t3 $t3 4		     
	move $t0 $t2
	bgt $t6 0 bDivBase           # while quotient > 0, divide by new base

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