Wrong result in multiplying in 8086 assembly - arrays

Question

The program must calculate the following:
in VP array , each index will have the value of Multiplying V1[INDEX] WITH V2[INDEX]
in VPROD array , the program ADDS all the Values of Array VP
Example:
VP = { V1[0]*V2[0] , V1[1]*V2[1] , V1[2]*V2[2] , V1[3]*V2[3] ,V1[4]*V2[4] }
VPROD = { VP[0] + VP[1] + VP[2] + VP[3] + VP[4] }
The problem is that when the result is bigger than 16 bits (a word), it does not give the right results. But when the result is smaller than 16 bits, it gives the right result.
I thought about Carry and fixed my code, but still it gives me bad results.
My code:
dseg segment
v1 DW 255,5,255,9,21
v2 DW 4,4,255,13,5
vprod DW 10 DUP (0)
vp DW 10 DUP (?)
N DB 5
dseg ends
sseg segment stack
dw 100h dup(?)
sseg ends
cseg segment
assume ds:dseg,cs:cseg,ss:sseg
start: mov ax,dseg
MOV DS,AX
MOV SI,0
MOV CX,0
MOV CL,N
MOV DI, 0
LOVP: MOV AX,v1[si]
MUL v2[si]
MOV vp[di],AX
MOV vp[di+2],DX
ADD SI,2
ADD DI,4
LOOP LOVP
MOV CX,0
MOV CL,N
MOV SI,0
MOV DI,0
LOVPROD: MOV AX,vp[SI]
ADD vprod[DI],AX
ADC VPROD[DI+2],0
ADD SI,2
LOOP LOVPROD
SOF:
mov ah,4ch
int 21h
cseg ends
end start

Answer 1

Since you are getting a 32 bit result from the multiply, you should use 4 bytes for every element of the vp array. You will need to use a separate index for that, and of course store the high word at offset +2 instead of +1. For the summation part, you should add up both low and high words.
Fixed code for the multiplication could look like:
MOV DI, 0
LOVP: MOV AX,v1[si]
MUL v2[si]
MOV vp[di],AX
MOV vp[di+2],DX
ADD SI,2
ADD DI,4
LOOP LOVP
I trust you can do the summation yourself, using ADD and ADC.
UPDATE:
Since your post says you want to sum the vp array, I don't see why you expect the result in another array (vprod). The sum is a scalar value, do something like:
MOV SI, 0
MOV AX, 0
MOV DX, 0
LOVPROD: ADD AX,vp[SI]
ADC DX,vp[SI+2]
ADD SI,4
LOOP LOVPROD
The result will be in DX:AX
Also, for the LOOP to work properly, you should put the number of iterations into CX, not 0 as you are doing.