8085 program to find the sum of first n natural numbers
Problem – Write an assembly language program for calculating the sum of first n natural numbers using 8085 microprocessor.
Example –
Input : 04H Output : 0AH as 01+02+03+04 = 10 in decimal => 0AH
The formula for calculating the sum of first n natural numbers is .
Algorithm –
- With n as the input, increment it to obtain n+1.
- Multiply n with n+1.
- Divide the product obtained by 2.
In 8085 microprocessor, no direct instruction exists to multiply two numbers, so multiplication is done by repeated addition as 4×5 is equivalent to 4+4+4+4+4 (i.e., 5 times).
Input: 04H
Add 04H 5 times
Product: 14H(2010)
Similarly, in 8085 microprocessor, no direct instruction exists to divide two numbers, so division is done by repeated subtraction.
Input: 14H
Keep subtracting 2 from the input till it reduces to 0.
Since subtraction has to be performed 1010 times before 14H becomes 0, the quotient is 1010 => 0AH.
Steps –
- Load the data from the memory location (201BH, arbitrary choice) into the accumulator
- Move this data into B
- Increment the value in the accumulator by one and move it to the register C
- Initialise the accumulator with 0
- Multiplication: Keep adding B to accumulator. The number of times B has to be added is equal to the value of C
- Initialise B with 00H. B will store the quotient of the division
- Initialise C with 02H. This is the divisor for the division
- Division: Keep subtracting C from A till A becomes 0. For each subtraction, increment B by one
- The final answer is in B. Move it to A. Then store the value of A in 201CH (arbitrary choice again)
201CH contains the final answer.
ADDRESS | LABEL | MNEMONIC |
---|---|---|
2000H | LDA 201BH | |
2001H | ||
2002H | ||
2003H | MOV B, A | |
2004H | INR A | |
2005H | MOV C, A | |
2006H | MVI A, 00H | |
2007H | ||
2008H | LOOP1 | ADD B |
2009H | DCR C | |
200AH | JNZ LOOP1 | |
200BH | ||
200CH | ||
200DH | MVI C, 02H | |
200EH | ||
200FH | MVI B, 00H | |
2010H | ||
2011H | LOOP2 | INR B |
2012H | SUB C | |
2013H | JNZ LOOP2 | |
2014H | ||
2015H | ||
2016H | MOV A, B | |
2017H | STA 201CH | |
2018H | ||
2019H | ||
201AH | HLT |
Store the value of n in 201BH. The sum can be found at 201CH.