Presenting here two implementations of a counter.

### What does the counter do?

Given a base

*n,*this counter will allow you to do base*n*counting. What's base-*n*counting? There are*n*digits: 0, 1, 2, ...,*n -*1. At each place, the digit changes from*i*to*i +*1 if*i < n -*1, and to 0 if*i = n -*1. This change happens when the change at that place is*triggered.*And when does the trigger happen. For the unit's place, the trigger happens whenever the function is called. For all other places, the trigger happens when the previous place's digit rolls over from*n*- 1 to 0. That's all. That's a bit technical description for the simple act of counting we learn in our KG. But if we want to implement the counter, it needs to be written in this algorithmic language.
A 3-bit binary (base-2) counter goes like:

**000, 001, 010, 011, 100, 101, 110, 111, 000, ...**

A 2-digit base-4 counter would count as:

**00, 01, 02, 03, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 00, ...**

What do we usually do in day-to-day counting? decimal (base-10) counting.

### How do we Use the Counter Program?

###
Below is a piece of code that could be used to implement a binary counter on a 3-bit number.

Below is a piece of code that could be used to implement a binary counter on a 3-bit number.

base = 2 inc = makeCounter_iter(base) n = [0, 0, 0] print n for i in range(base ** len(n)): n = inc(n) print n

The

**inc(n)**gives**n + 1**in the base n number system which is pre-decided while instantiating the counter:
base = 2

#!/usr/bin/python def makeCounter_iter(base): def isZero(lst): return lst == [0] * len(lst) def inc(num): if(len(num) > 1): rem = inc(num[:-1]) if(isZero(rem)): if(num[-1] == base - 1): rem.extend([0]) else: rem.extend([num[-1] + 1]) else: rem.extend([num[-1]]) return rem else: new = [0] if(not num[0] == base - 1): new[0] = num[0] + 1 return new return inc

Now follows the recursive version.

#!/usr/bin/python def makeCounter_rec(base): def incDigit(num, pos): new = num[:] if(num[pos] == base - 1): new[pos] = 0 if(pos < len(num) - 1): return incDigit(new, pos + 1) else: new[pos] = new[pos] + 1 return new def inc(num): return incDigit(num, 0) return inc

Any day, the recursive implementation trumps over the iterative version. The recursive implementation is smaller and more readable because it's very like the way the process of counting is formally defined in the beginning of the article.

### Functional Programming Flavour

One thing to notice is that we use functional language aspect of python. The function

**makeCounter**(**makeCounter_iter**and**makeCounter_rec**) is a*higher order function*that returns another function inc, the increment function. Also, the value of base is fixed in the creation context of inc inside the makeCounter function. The inc function uses the value of base at a place in the code which is typically outside the lexical scope where base is defined. This is known as the*closure*feature of functional programming. In a typical*object-oriented*scenario, this effect is achieved using the*builder design pattern*.
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