Add the least-significant addends together, generating and saving the carry bit. Do not use the previous value of the carry bit in this initial addition operation -- clear it if necessitated by the instruction set.

Then add the next-least-significant words together both using the carry from the previous addition, and generating carry for the next addition.

Continue working your way through the most-significant words. If adding those most-significant words generates a carry, don't forget to include it in the final result! -- Well, unless it exceeds the number of bits you're allowed to output, in which case you should call it an error.

I assume that the input and output numbers don't need to be converted from/to decimal, and that both input numbers are positive.

Jim

.section ".data"
format: .asciz "%s%c"
displayformat: .asciz "%d\n"
prompt1: .asciz "Enter first number (100 digit max): "
prompt2: .asciz "Enter second number (100 digit max): "
sDisplaySum: .asciz "\nThe sum is: %d"
sDisplayDiff: .asciz "\nThe difference is: %d"
nl: .byte '\n'

.align 4
.section ".bss"
input1: .skip 4 * 50
input2: .skip 4 * 50
sum: .skip 4 * 50
diff: .skip 4 * 50

.align 4
findSumDiff:
save %sp, -96, %sp!can not be leaf b/c must call validate subroutine

!use a loop to continue to load .words and check each time to see if %l1 and %l2 are 0
!use addxcc and 
mov 0, %l3!set byte counter to loop

set input1, %l0!load first 32 bits to add
ld [%l0 + %l3], %l1!first number

set input2, %l0!load first 32 bits to add
ld [%l0 + %l3], %l2!second number

addcc %l1, %l2, %l4!does first add and sets the carry flag

set sum, %l5
st %l4, [%l5 + %l3]!store the first part of the sum into memory

add %l3, 4, %l3!increment counter

addloop:
set input1, %l0!loads the next 32 bits of first number
ld [%l0 + %l3], %l1

set input2, %l0!loads the next 32 bits of second number
ld [%l0 + %l3], %l2

addxcc %l1, %l2, %l4!adds in carry to the addition, adds, then sets the flag again

set sum, %l5
st %l4, [%l5 + %l3]!store the first part of the sum into memory

add %l3, 4, %l3!increments counter again

cmp %l3, 200
bne addloop
nop

ret
restore

So, I can't help you with whether your code works or not (Don't you have access to a machine to debug it on? If not, you should be able to get an emulator.)

But I am suspicious of the word "digit" in the description of the problem.

Are you sure you aren't supposed to be doing BCD arithmetic, rather than binary?