In Mathematics, the factorial of n is denoted by n! and calculated by the product of integer numbers from 1 to n.

For instance:

In this challenge you will write a program using Little Man Computer to ask the user to enter a positive number. In return the program will output the factorial of this number.

Before completing this challenge, we recommend you to have a go at:

• Little Man Computer: Multiplication
• Little Man Computer: 5 + 4 + 3 + 2+ 1

Multiplication using LMC

While checking the Little Man Computer Instruction Set (See table at the bottom of this post), you will have noticed that, through there are two instructions for adding (ADD) and subtracting (SUB) numbers, there is no instruction for multiplying two numbers.

The solution to overcome this, is two consider a multiplication as a series of additions. For instance:

5 * 4 = 5 + 5 + 5 + 5

Find out more: Little Man Computer: Multiplication

Iteration using LMC

To apply an iterative approach for this challenge we will use branching options: Little Man Computer: 5 + 4 + 3 + 2+ 1.

This challenge will add a level of complexity as we will be using a nested loop approach: one loop to list all the multiplications to be performed (e.g. 4! = 4 * 3 * 2 * 1) and one loop for implementing each multiplication as a series of additions. (e.g. 4 * 3 = 4 + 4 + 4)

LMC Simulators

• Online LMC Simulator
• Alternative LMC Simulator

Solution

This solution also caters for the fact that 0! = 1. This is the purpose of line 3, 34,35 and 36.

          inp 
          sta final 
          brz oneval
          sub one
          sta iteration
          sta counter
          lda final
          sta num
mult      lda iteration
          brz end
          sub one
          brz end
          lda final
          add num
          sta final
          lda counter
          sub one
          sta counter
          sub one
          brz next
          bra mult
next      lda final
          sta num 
          lda iteration
          sub one
          sta iteration
          sta counter
          sub one
          brz end
          bra mult
end       lda final
          out
          hlt
oneval    lda one
          out
          hlt
final     dat 0
counter   dat 0
one       dat 1
iteration dat 0
num       dat 0

LMC Instruction Set

Note that in the following table “xx” refers to a memory address (aka mailbox) in the RAM. The online LMC simulator has 100 different mailboxes in the RAM ranging from 00 to 99.

Mnemonic	Name	Description	Op Code
INP	INPUT	Retrieve user input and stores it in the accumulator.	901
OUT	OUTPUT	Output the value stored in the accumulator.	902
LDA	LOAD	Load the Accumulator with the contents of the memory address given.	5xx
STA	STORE	Store the value in the Accumulator in the memory address given.	3xx
ADD	ADD	Add the contents of the memory address to the Accumulator	1xx
SUB	SUBTRACT	Subtract the contents of the memory address from the Accumulator	2xx
BRP	BRANCH IF POSITIVE	Branch/Jump to the address given if the Accumulator is zero or positive.	8xx
BRZ	BRANCH IF ZERO	Branch/Jump to the address given if the Accumulator is zero.	7xx
BRA	BRANCH ALWAYS	Branch/Jump to the address given.	6xx
HLT	HALT	Stop the code	000
DAT	DATA LOCATION	Used to associate a label to a free memory address. An optional value can also be used to be stored at the memory address.

Write an LMC program to let the user enter two numbers, num1 and num2.
The program should output the results of multiplying these two numbers: num1 x num2.

LMC Simulators

• Online LMC Simulator
• Alternative LMC Simulator

Solution

While checking the Little Man Computer Instruction Set (See table at the bottom of this post), you will have noticed that, through there are two instructions for adding (ADD) and subtracting (SUB) numbers, there is no instruction for multiplying two numbers.

The solution to overcome this, is two consider a multiplication as a series of additions. For instance:

5 * 4 = 5 + 5 + 5 + 5

This is how we will implement our multiplication algorithm:

        INP
        STA NUM1
        INP 
        STA NUM2
LOOP    LDA TOTAL
        ADD NUM1
        STA TOTAL
        LDA NUM2
        SUB ONE
        STA NUM2
        BRP LOOP
        LDA TOTAL
        SUB NUM1
        STA TOTAL
        OUT
        HLT
NUM1    DAT
NUM2    DAT
ONE     DAT 1
TOTAL   DAT 0

LMC Instruction Set

Note that in the following table “xx” refers to a memory address (aka mailbox) in the RAM. The online LMC simulator has 100 different mailboxes in the RAM ranging from 00 to 99.

Mnemonic	Name	Description	Op Code
INP	INPUT	Retrieve user input and stores it in the accumulator.	901
OUT	OUTPUT	Output the value stored in the accumulator.	902
LDA	LOAD	Load the Accumulator with the contents of the memory address given.	5xx
STA	STORE	Store the value in the Accumulator in the memory address given.	3xx
ADD	ADD	Add the contents of the memory address to the Accumulator	1xx
SUB	SUBTRACT	Subtract the contents of the memory address from the Accumulator	2xx
BRP	BRANCH IF POSITIVE	Branch/Jump to the address given if the Accumulator is zero or positive.	8xx
BRZ	BRANCH IF ZERO	Branch/Jump to the address given if the Accumulator is zero.	7xx
BRA	BRANCH ALWAYS	Branch/Jump to the address given.	6xx
HLT	HALT	Stop the code	000
DAT	DATA LOCATION	Used to associate a label to a free memory address. An optional value can also be used to be stored at the memory address.

Write an LMC program to let the user enter a number n.

The program should calculate the output n + (n-1) + (n-2) + … + 3 + 2 + 1.

For instance if the user enters the value 5. The program should output the number 15 because:

5 + 4 + 3 + 2 + 1 = 15

LMC Simulators

• Online LMC Simulator
• Alternative LMC Simulator

Solution

LMC Instruction Set

Note that in the following table “xx” refers to a memory address (aka mailbox) in the RAM. The online LMC simulator has 100 different mailboxes in the RAM ranging from 00 to 99.

Mnemonic	Name	Description	Op Code
INP	INPUT	Retrieve user input and stores it in the accumulator.	901
OUT	OUTPUT	Output the value stored in the accumulator.	902
LDA	LOAD	Load the Accumulator with the contents of the memory address given.	5xx
STA	STORE	Store the value in the Accumulator in the memory address given.	3xx
ADD	ADD	Add the contents of the memory address to the Accumulator	1xx
SUB	SUBTRACT	Subtract the contents of the memory address from the Accumulator	2xx
BRP	BRANCH IF POSITIVE	Branch/Jump to the address given if the Accumulator is zero or positive.	8xx
BRZ	BRANCH IF ZERO	Branch/Jump to the address given if the Accumulator is zero.	7xx
BRA	BRANCH ALWAYS	Branch/Jump to the address given.	6xx
HLT	HALT	Stop the code	000
DAT	DATA LOCATION	Used to associate a label to a free memory address. An optional value can also be used to be stored at the memory address.