Little Man Computer: Factorial Challenge

arithmetic-quiz-calculatorIn Mathematics, the factorial of n is denoted by n! and calculated by the product of integer numbers from 1 to n.

For instance:
factorial-of-5

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:

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 Simulator


Online LMC Simulator

Solution


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

© Solution by Howard C.

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.
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