# ASSEMBLY16 An Assembly program to find nCr for given n and r

By | March 18, 2014

Now we will write another Assembly program to find nCr for given n and r

Let’s identify variables needed for this program.
First variables will be the one which will hold the value entered by user in the variable and variable R.DIFF will hold Difference between N and R. In nCr N is always Greater than R so the difference will be N-R. NN variable will hold N!, RR variable will hold R! NR variable will hold (N-R)! FACT will hold 1H and Other variable RES will be holding the Resultant Decimal equivalent printable form to be printed for the User on Screen and Other variables will be holding the Messages “ENTER N: \$”, “ENTER R: \$”, “N > R (NOT ALLOWED) !!! \$” and “RESULT : \$”  to be printed for the User, So in all Twelve variables.
The identified variables are N, R, DIFF, NN, RR,NR, FACT, RES, MSG1, MSG2, MSG3 and MSG4.

First Line – DATA SEGMENT

DATA SEGMENT is the starting point of the Data Segment in a Program and DATA is the name given to this segment and SEGMENT is the keyword for defining Segments, Where we can declare our variables.

Next Line – N DB ?
R DB ?
DIFF DB ?
NN DW ?
RR DW ?
NR DW ?
FACT DW 1H
RES DB 10 DUP (‘\$’)
MSG1 DB “ENTER R : \$”
MSG2 DB 10,13,”ENTER N : \$”
MSG3 DB 10,13,”RESULT : \$”
MSG4 DB 10,13,”N > R (NOT ALLOWED) !!! \$”

N DB ?, R DB ?, DIFF DB ?, NN DW ?, RR DW ?, NR DW ?  We are initializing ALL to ? (? stands for blank value), As we are accepting value from User from Console as the Decimal number to find Factorial of it. Detailed explanation is given below. FACT DB 1H We are initializing FACT to 1H (H stands for Hexadecimal value). RES  DB 10 DUP (‘\$’) this line is a declaration of Array initialized with ‘\$’ which works as New Line Character. \$ is used as (\n) NULL character in C program. (A Number Character is of a BYTE size Hence we have to used only DB Define Byte ) as we don’t know the lenght of the digits in the Resultant Decimal equivalent printable form, Therefore we take it approx size ten. Here 10 DUP (‘\$’) stands for N i.e. Size of Array or Array Size. DUP stands for Duplicate i.e. it will duplicate the value in All the Array with the value present in Bracket (i.e. \$). MSG1 DB “ENTER NUMBER: \$” this line is a declaration of Charater Array initialized with “ENTER NUMBER:\$” and \$ is used as (\n) NULL character in C program. (A Character is of a BYTE Hence we have to use only DB Define Byte ). MSG2 DB 10,13,”ENTER N : \$”, MSG3 DB 10,13,”RESULT : \$”
MSG4 DB 10,13,”N > R (NOT ALLOWED) !!! \$” this line is a declaration of Charater Array initialized with “RESULT:  \$”. 10,13, works as New Line Character if this is not present All the Messages will be printed on the same line and \$ is used as (\n) NULL character in C program. (A Character is of a BYTE Hence we have to use only DB Define Byte ).

Next Line – DATA ENDS

DATA ENDS is the End point of the Data Segment in a Program. We can write just ENDS But to differentiate the end of which segment it is of which we have to write the same name given to the Data Segment.

Now, Selection of data type is DB data type the numbers which we are adding will be integers so DB is sufficient, and the variables holding Factorials to numbers are assigned to DW data type, As they hold bigger values.

 Source code
```DATA SEGMENT
N DB ?
R DB ?
DIFF DB ?
NN DW ?
RR DW ?
NR DW ?
FACT DW 1H
RES DB 10 DUP ('\$')
MSG1 DB "ENTER R : \$"
MSG2 DB 10,13,"ENTER N : \$"
MSG3 DB 10,13,"RESULT : \$"
MSG4 DB 10,13,"N > R (NOT ALLOWED) !!! \$"
DATA ENDS```

In Assembly programming, the variable are all defined by bytes only.

DB – Define Byte  (Size – 1 Byte)

DW – Define Word  (Size – 2 Byte)

DD – Define Double word  (Size –  4 Bytes)

DQ – Define Quad word  (Size – 8 Bytes)

DT – Define Ten Bytes  (Size – 10 Bytes)

NUMBER SYSTEM in Assembly Programming is Decimal, Octal, Hexadecimal, Binary.

In the Program, We are entering the values for the variables and Do arithmetical Operations like Addition, Subtraction, Multiplication and Division So the Computer should understand which kind of Number is entered. Hence there is a different letters for different Number Systems. O or o stands for Octal, H or h stands for Hexadecimal, B or b stands for Binary, D or d stands for Decimal. By default type of numbering system is Decimal. If you do not specify any letter then the number is understood to be Decimal (By default).

 Source code
```DATA SEGMENT
N DB ?
R DB ?
DIFF DB ?
NN DW ?
RR DW ?
NR DW ?
FACT DW 1H
RES DB 10 DUP ('\$')
MSG1 DB "ENTER R : \$"
MSG2 DB 10,13,"ENTER N : \$"
MSG3 DB 10,13,"RESULT : \$"
MSG4 DB 10,13,"N > R (NOT ALLOWED) !!! \$"
DATA ENDS
CODE SEGMENT
ASSUME DS:DATA,CS:CODE
START:
MOV AX,DATA
MOV DS,AX
LEA DX,MSG1
MOV AH,9
INT 21H
MOV AH,1
INT 21H
SUB AL,30H
MOV R,AL
LEA DX,MSG2
MOV AH,9
INT 21H
MOV AH,1
INT 21H
SUB AL,30H
MOV N,AL
SUB AL,R
MOV DIFF,AL
CMP AL,0
JL LABEL4
MOV AX,FACT
MOV CH,0
MOV CL,N
LABEL1: MUL CL
LOOP LABEL1
MOV NN,AX
MOV AX,FACT
MOV CH,0
MOV CL,R
LABEL2: MUL CL
LOOP LABEL2
MOV RR,AX
MOV AX,FACT
MOV CH,0
MOV CL,DIFF
LABEL3: MUL CL
LOOP LABEL3
MOV NR,AX
MOV DX,0
MOV BX,RR
MUL BX
MOV BX,AX
MOV DX,0
MOV AX,NN
DIV BX
LEA SI,RES
CALL HEX2DEC
LEA DX,MSG3
MOV AH,9
INT 21H
LEA DX,RES
MOV AH,9
INT 21H
JMP EXIT
LABEL4: LEA DX,MSG4
MOV AH,9
INT 21H
EXIT: MOV AH,4CH
INT 21H
CODE ENDS
HEX2DEC PROC NEAR
MOV CX,0
MOV BX,10
LOOP1: MOV DX,0
DIV BX
PUSH DX
INC CX
CMP AX,9
JG LOOP1
MOV [SI],AL
LOOP2: POP AX
INC SI
MOV [SI],AL
LOOP LOOP2
RET
HEX2DEC ENDP
END START```

Explanation :

In this Assembly Language Programming, A single program is divided into four Segments which are 1. Data Segment, 2. Code Segment, 3. Stack Segment, and 4. Extra  Segment. Now, from these one is compulsory i.e. Code Segment if at all you don’t need variable(s) for your program.if you need variable(s) for your program you will need two Segments i.e. Code Segment and Data Segment.

Next Line –CODE SEGMENT

CODE SEGMENT is the starting point of the Code Segment in a Program and CODE is the name given to this segment and SEGMENT is the keyword for defining Segments, Where we can write the coding of the program.

Next Line –     ASSUME DS:DATA CS:CODE

In this Assembly Language Programming, their are Different Registers present for Different Purpose So we have to assume DATA is the name given to Data Segment register and CODE is the name given to Code Segment register (SS,ES are used in the same way as CS,DS )

Next Line – START:

START is the label used to show the starting point of the code which is written in the Code Segment. : is used to define a label as in C programming.

Next Line – MOV AX,DATA
MOV DS,AX

After Assuming DATA and CODE Segment, Still it is compulsory to initialize Data Segment to DS register.  MOV is a keyword to move the second element into the first element. But we cannot move DATA Directly to DS due to MOV commands restriction, Hence we move DATA to AX and then from AX to DS. AX is the first and most important register in the ALU unit. This part is also called INITIALIZATION OF DATA SEGMENT and It is important so that the Data elements or variables in the DATA Segment are made accessable. Other Segments are not needed to be initialized, Only assuming is enhalf.

Next Line – LEA DX,MSG1
MOV AH,9
INT 21H

The above three line code is used to print String or Message present in the character Array till \$  symbol which tells the compiler to stop.

Now, lets understand line by line

LEA DX,MSG1 in this LEA stands for LOAD EFFECTIVE ADDRESS and it loads the effective address of second element into the first element.  This same code can be interchangably written as MOV DX, OFFSET MSG1 where OFFSET  means effective address and MOV means move  second element into the first element.

MOV AH,9
INT 21H

The above two line code is used to PRINT the String or Message of the address present in DX register.

Standard Input and Standard Output related Interupts are found in INT 21H which is also called as DOS interrupt. It works with the value of AH register, If the Value is 9 or 9h, That means PRINT the String or Message of the address present in DX register.

Next Line – MOV AH,1
INT 21H

The above three line code is used to Read a Character from Console and save the value entered in variable R in its ASCII form.

Standard Input and Standard Output related Interupts are found in INT 21H which is also called as DOS interrupt. It works with the value of AH register, If the Value is 1 or 1h, That means READ a Character from Console, Echo it on screen and save the value entered in AL register.

Next Line – SUB AL,30H
MOV R,AL

The above Two line code is used to convert the value entered in variable R from ASCII form to its BCD form. This can be done by subtracting 30H i.e. SUB AL,30H. The value coming from Console is Basically in ASCII form. eg. When you enter 5 we see 35H,So by subtracting 30H we get back to value as 5. SUB AL,30H means subtracting 30H from AL. MOV R,AL  means move value in AL register into variable R.

Next Line – LEA DX,MSG2
MOV AH,9
INT 21H

MOV AH,1
INT 21H
SUB AL,30H
MOV N,AL

Same as above to scan N from the Console (Screen) entered by User.

Next Line – SUB AL,R
MOV DIFF,AL

SUB AL,R means subtracting value of variable R from AL register in which value of variable N is present. MOV DIFF,AL  means move value in AL register into variable DIFF.

Next Line – CMP AL,0
JL LABEL4

The above two line code is used to Compare and Jump if AL is Less Than Zero.

CMP AL,0 is used to Compare entered value i.e. AL register with Zero. JL LABEL4 is used to Jump to Label LABEL4 if if AL is Less Than Zero when compared with CMP instruction prior to this one.

Next Line – MOV AX,FACT
MOV CH,0
MOV CL,N

MOV AX,FACT means move value in AL register from variable FACT. MOV CH,0 is used to clear the unwanted value (garbage value) in AH register is removed by assigning ZERO to it. MOV CL,N  means move value in AL register from variable N.

In assembly programming language we have a LOOP instruction. This works with two other helpers which are Label and Counter. The Loop start with LABEL and ends with LOOP instruction with the same LABEL name with it. the execution of the Loop depends on the value in CX register ( CX is also Called COUNTER).

Next Line – LABEL1:

LABEL1: is a LABEL and all the words ending in colon (:).

Next Line – MUL CL

The above line code is used to Multiply CL with AX register  i.e.Value present in AX register

Next Line – LOOP INPUT

This end of loop. In assembly programming language we have a LOOP instruction. This works with two other helpers which are Label and Counter. The Loop start with LABEL and ends with LOOP instruction with the same LABEL name with it. the execution of the Loop depends on the value in CX register ( CX is also Called COUNTER).

Next Line – MOV NN,AX

MOV NN,AX means move value in AX register to variable NN. The value present in AX register is Factorial of variable N.

Next Line –  MOV AX,FACT
MOV CH,0
MOV CL,R

LABEL2: MUL CL
LOOP LABEL2

MOV RR,AX

Same as above to generate Factorial of variable R and Save as RR.

Next Line –  MOV AX,FACT
MOV CH,0
MOV CL,DIFF

LABEL3: MUL CL
LOOP LABEL3

MOV NR,AX

Same as above to generate Factorial of Difference of variable N and R and Save as NR.

Now, Let me tell you Formula of nCr :- n!/( n!(n-r)! ).

Next Line – MOV DX,0
MOV BX,RR
MUL BX
MOV BX,AX

MOV DX,0 is used to clear the unwanted value (garbage value) in DX register is removed by assigning ZERO to it. MOV BX,RR means move value in AX register from variable RR. The value present in variable RR is Factorial of R. MUL BX  in this line BX register will be Multiplied with AX:DX register (BY DEFAULT) in which the resultant value of (N-R)! is present. Now, This will give R!(N-R)!. MOV BX,AX move value in BX register from AX register and use it later.

Next Line – MOV DX,0
MOV AX,NN
DIV BX

MOV DX,0 is used to clear the unwanted value (garbage value) in DX register is removed by assigning ZERO to it. MOV AX,NN means move value in AX register from variable NN. The value present in variable NN is Factorial of N. DIV BX in this line value in BX register will Divide  AX:DX register (BY DEFAULT) in which the resultant value of N! is present. Now, This will give N!/(R!(N-R)!) which is Result.

Next Line – LEA SI,RES
CALL HEX2DEC

The above Two line code is used to initialize RES to SI register and Call Procedure HEX2DEC which will covert AX register value as result and Print it on user screen.

LEA SI,RES is used to Load Effective Address of RES variable to SI Register.

CALL HEX2DEC is used to Call a Procedure named HEX2DEC

Next Line – LEA DX,MSG2
MOV AH,9
INT 21H

The above two line code is used to PRINT the String or Message of the address present in DX register i.e. for MSG2.

Next Line – LEA DX,RES
MOV AH,9
INT 21H

The above three line code is used to print String or Message present in the character Array till \$  symbol which tells the compiler to stop. As we have initialized all the values in an Array to \$ you will think what will be printed. The procedure is going to change the Array to its Resultant Decimal equivalent printable form i.e. ASCII form of a digit number.

Now, lets understand line by line

LEA DX,RES in this LEA stands for LOAD EFFECTIVE ADDRESS and it loads the effective address of second element into the first element.  This same code can be interchangably written as MOV DX, OFFSET RES where OFFSET  means effective address and MOV means move  second element into the first element.

MOV AH,9
INT 21H

The above two line code is used to PRINT the String or Message of the address present in DX register.

Standard Input and Standard Output related Interupts are found in INT 21H which is also called as DOS interrupt. It works with the value of AH register, If the Value is 9 or 9h, That means PRINT the String or Message of the address present in DX register.

Next Line – JMP EXIT

The above line code is used to Jump to Label EXIT without any condition check. This jump will basically SKIP printing of ERROR Message  from execution.

Next Line – LABEL4: LEA DX,MSG4
MOV AH,9
INT 21H

The above three line code is used to PRINT the String or Message of the address present in DX register i.e. for MSG4 which is ERROR message.

Next Line – EXIT: MOV AH,4CH
INT 21H

The above two line code is used to exit to dos or exit to operating system. Standard Input and Standard Output related Interupts are found in INT 21H which is also called as DOS interrupt. It works with the value of AH register, If the Value is 4ch, That means Return to Operating System or DOS which is the End of the program.

Next Line – CODE ENDS

CODE ENDS is the End point of the Code Segment in a Program. We can write just ENDS But to differentiate the end of which segment it is of which we have to write the same name given to the Code Segment.

PROCEDURE Code starts here:

Procedure is a part of code that can be called from a program in order to perform specific task.

Next Line – HEX2DEC PROC NEAR

This line of code is used to start a procedure code and we can make out the procedure by the keyword PROC which tells us the procedure is started. In assembly language we have two types of Procedures one is NEAR and other is FAR. NEAR is used to call the Procedure within the program whereas FAR is used to call the procedure outside the program. HEX2DEC is only the Name given to the Procedure Code.

Next Line –  MOV CX,0
MOV BX,10

MOV CX,0 is used to move or assign value 0 (decimal value) to  CX. The program which we are wishing to write is to covert HexaDecimal value to Decimal value, In which we will divide the number till the Quotient is going to be Zero. CX register ( CX is also Called COUNTER). CX register will count the number digit generated by dividing the Hexadecimal number by Base value of Decimal i.e.Ten. MOV BX,10 in this Base value 10 is moved to BX register, So that it is used to divide hexa number by 10.

Next Line – LOOP1: MOV DX,0

LOOP1: is a LABEL and all the words ending in colon (:) are Labels. MOV DX,0 is used to clear the unwanted value (garbage value) in DX register is removed by assigning ZERO to it. First Loop starts here.

Next Line – DIV BX

DIV instruction only works with REG or MEMORY hence we cannot use DIV 10 where 10 is immediate, So we have to move 10 to BX register (we can take any register) this we have already done above and Then DIV BX  Now DIV BX will Divide AX register with 10 which is passed to BX register and Result of division is present in AX register contains Quotientand DX register contains Remainder. Here we will not touch Quotient AX as it will be used for furture Division, But DX Remainder will be Decimal Digit and will always be less than Ten so the value will be in DL register only and to make it printable on Console (Screen) we have to add  30H So that it will become a ASCII character and will be saved in Charater Array and will be printed as String later So ADD DL,30H.

Next Line – PUSH DX
INC CX

PUSH is a stack function. Stack is an area of memory for keeping temporary data. PUSH and POP are two stack operations which stores or gets 16 bits of data. PUSH DX stores 16 bit data inside DX register into Stack Area. INC is a instruction for Increment the present in Register or Memory. INC CX will increment the value present in CX register by One. Here we are using CX register as a counter and counting the numbers of digits in their ASCII form which are pushed into Stack. So that the same count will help to POP the values out of Stack.

Next Line – MOV CX,10

MOV CX,10 is used to move or assign value 10 (decimal value) to  CX. The program which we are wishing to write is to input ten characters from console which will be entered by the user, Hence to do so we need a loop construct. In assembly programming language we have a LOOP instruction. This works with two other helpers which are Label and Counter. The Loop start with LABEL and ends with LOOP instruction with the same LABEL name with it. the execution of the Loop depends on the value in CX register ( CX is also Called COUNTER).

Next Line – CMP AX,9
JG LOOP1

CMP AX,9  is used to compare AX register with 9 and jump if AX is greater to the respective LABEL LOOP1. The result of Comparision is not stored anywhere, but flags are set according to result.  is Short Jump if first operand is Greater then second operand (as set by CMP instruction). Signed. SECOND is the label where the compiler will JUMP. First Loop ends here. Note :- this loop is without LOOP keyword and depends upon the number to be converted.

MOV [SI],AL

ADD AL,30H The Last Remainder will be Decimal Digit in AX register only as the number cannot be divided future and will always be less than Ten so the value will be in AL register only and to make it printable on Console (Screen) we have to add  30H So that it will become a ASCII character and will be saved in Charater Array and will be printed as String later. MOV [SI],AL Saving the Characters in Character Array (i.e. String) is done by Moving AL register to Address of SI register which is represented in Square Brackets i.e. [SI]. SI is assigned with the Character Array i.e. RES.

Next Line – LOOP2: POP AX
INC SI

LOOP2: is a LABEL and all the words ending in colon (:) are Labels. POP is a stack function. Stack is an area of memory for keeping temporary data. PUSH and POP are two stack operations which stores or gets 16 bits of data. POP AX gets 16 bit data to AX register from Top of Stack. INC CX will increment the value present in CX register by One. Here we are using CX register as a counter and counting the numbers of digits in their ASCII form which are pushed into Stack. So that the same count will help to POP the values out of Stack and save it in AX register. Second Loop starts here.

Next Line – MOV [SI],AL

The values out of Stack saved in AX register saved in string in this Loop. MOV [SI],AL Saving the Characters in Character Array (i.e. String) is done by Moving AL register to Address of SI register which is represented in Square Brackets i.e. [SI]. SI is assigned with the Character Array i.e. RES.

Next Line – LOOP LOOP2

This end of loop. In assembly programming language we have a LOOP instruction. This works with two other helpers which are Label and Counter. The Loop start with LABEL and ends with LOOP instruction with the same LABEL name with it. the execution of the Loop depends on the value in CX register ( CX is also Called COUNTER).

Next Line – RET

RET is a return instruction. This instruction is used only if  the control is been passed to the code outside Main like to Procedure. this return the control to the place where the Procudure was called.

Next Line – HEX2DEC ENDP

HEX2DEC ENDP is the End point of the Procedure in a Program.

This line of code is used to end the procedure code and we can make out the procedure by the keyword ENDP which tells us the procedure is ended. In assembly language we have two types of Procedures one is NEAR and other is FAR. NEAR is used to call the Procedure within the program whereas FAR is used to call the procedure outside the program. HEX2DEC is only the Name given to the Procedure Code.

Last Line – END START

END START is the end of the label used to show the ending point of the code which is written in the Code Segment.

Note :- In this Assembly Language Programming, We have Com format and EXE format. We are Learning in EXE format only which simple then COM format to understand and Write. We can write the program in lower or upper case, But i prepare Upper Case.

Screen Shots :-

Output After Execution :-

Note :- To see the variable and its value you have to click vars button in the emulator.

Note:- To understand program for sequence in detail Please SEARCH numerically example: ASSEMBLY01, ASSEMBLY02, etc.

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