Code stuck at an infinite loop when finding the nth fibonacci number - loops

Question

I was trying to find the nth Fibonacci number e.x n=3, output = 1
so my logic was this
a = 0
b = 1
input n
si 0
n>2
loop
temp = b
b = a+b
a = b
loop if si/=cx
print b
This is my pseudo code logic. When I tried to implement this I am stuck in an infinite loop
.MODEL SMALL
.STACK 100h
.DATA
STRING0 DB 'Enter INDEX $'
.CODE
MAIN PROC
MOV AX,#DATA
MOV DS,AX
LEA DX, STRING0
MOV AH,9
INT 21H
MOV AH, 2
MOV DL,0AH ;NEW LINE
INT 21H
MOV DL,0DH
INT 21H
MOV AH,1
INT 21H
SUB CX,CX
MOV CL,AL
MOV SI,0
MOV AX,0
MOV BX,1
LOOP1:
PUSH BX
ADD BX,AX
POP AX
INC SI
LOOP LOOP1
MOV DX,BX
MOV AH,9
INT 21H
MAIN ENDP
END MAIN
I use EMU 4.08. The code us stuck at an infinite loop. I have no idea why
I did SUB cx,cx to move the AL value to CL and use CL as counter otherwise it gives me error that the code failed to send 8bit data to 16bit

Answer 1

I was trying to find the nth Fibonacci number e.x n=3, output = 1
From your example I understand that you consider the Fibonacci sequence to begin with 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
Fibonacci himself started his sequence from 1, 2, 3, 5, 8, ...
See the Wikipedia article https://en.wikipedia.org/wiki/Fibonacci_number
I didn't follow your pseudo code too much as it has flaws of its own!
Why your assembly program fails
You say your "code is stuck at an infinite loop", but that's not really the case. It is just that your loop executes an extra 50 iterations. The reason is that the DOS.GetCharacter function 01h gives you an ASCII code, that you have to convert into the digit that the pressed key represents. eg. If you press 3, DOS gives you AL=51, and you need to subtract 48 to obtain the inputted digit which is 3.
But wait, don't use this number 3 as your loop counter already! Since the 1st and 2nd Fibonacci numbers are known from the start, calculating the 3rd Fibonacci number requires just 1 iteration of the loop. Account for this and subtract 2 beforehand.
Once your program has found the answer you simply move the result from BX to DX, and expect the DOS.PrintString function 09h to output the number. It can't do that. It's a function that outputs a series of characters (so a string beginning at the address in DX), however your result is still a number in a register. You have to convert it into its textual representation. Displaying numbers with DOS has all the fine details about this conversion!
Next code allows the user to input a single-digit from 1 to 9
...
mov ah, 01h ; DOS.GetCharacter
int 21h ; -> AL = ["1","9"]
sub al, 48 ; -> AL = [1,9]
cbw ; -> AH = 0
mov cx, ax ; -> CX = [1,9]
xor ax, ax ; -> AX = 0
dec cx
jz PrintIt ; 1st Fib is 0
inc ax ; -> AX = 1
dec cx
jz PrintIt ; 2nd Fib is 1
cwd ; -> DX = 0
CalcIt: ; 3rd Fib and others
xchg ax, dx
add ax, dx
loop CalcIt
PrintIt: ; AX is at most 21 (because of the limited input)
aam
add ax, 3030h ; Conversion into text
xchg al, ah
cmp al, '0'
mov dh, 02h ; DOS.PrintCharacter
xchg ax, dx
je Ones
int 21h
Ones:
mov dl, dh
int 21h
Because in your program the output is very limited, I used a special code to display at most 2 digits. For the general case of outputting numbers see this Q/A.

Answer 2

I think this should be good:
.MODEL SMALL
.STACK 100h
.DATA
STRING0 DB 'Enter INDEX $'
STRING1 DB 'OUTPUT: $'
.CODE
MAIN PROC
MOV AX,#DATA
MOV DS,AX
LEA DX, STRING0
MOV AH,9
INT 21H
MOV AH, 2
MOV DL,0AH ;NEW LINE
INT 21H
MOV DL,0DH
INT 21H
MOV AH,1
INT 21H
SUB CX,CX
SUB AL,30H ;To convert char into digit value
MOV CL,AL
MOV SI,0
MOV AX,0
MOV BX,1
LOOP1:
PUSH BX
ADD BX,AX
POP AX
INC SI
LOOP LOOP1
MOV AH, 2
MOV DL,0AH ;NEW LINE
INT 21H
MOV DL,0DH
INT 21H
LEA DX, STRING1
MOV AH,9
INT 21H
;Print the result
MOV AX,BX
MOV SI,0
;Push digits from right to left into stack
LOOP2:
MOV DL,10
DIV DL
PUSH AX
MOV AH,0
INC SI
CMP AL,0
JNE LOOP2
;Pop digits from stack and print them
LOOP3:
POP DX
MOV DL,DH
MOV DH,0
ADD DL,30H ;To convert digit to char
MOV AH,2
INT 21H
DEC SI
CMP SI,0
JNE LOOP3
HLT
MAIN ENDP
END MAIN