Binary Pi, Anyone?

Computer Science Level 3

$\large \pi = 11.001001\dots$ Write $\pi$ in binary notation and consider the first 32 digits (i.e. digits after the binary point).

How many of these digits are "1"?

14 15 16 17 18

3 solutions

Khang Nguyen Thanh
Mar 18, 2016

$\pi=11.00100100\ 00111111\ 01101010\ 10001000\ 10000101\ 10100011\ ...$

Regarding how to do this by programming, here's a function definition written in Python 3 to print the binary representation of a non-negative number ( int or float ) :

def binf(n,d=10):
    k=int(n//1)
    n-=k
    l1=[]; l2=[]
    while k>0:
        l1=[str(k%2)]+l1
        k//=2
    count=1
    while n>0 and count<=d:
        l2+=[str(int(n*2**count))]
        if l2[-1]=='1': n-=2**(-count)
        count+=1
    if l2==[]: l2=['0']
    if l1==[]: l1=['0']
    return ''.join(l1)+'.'+''.join(l2)

Importing pi from math module of py3 (or just using a good enough approximation for $\pi$ ) and calling binf(pi,32) will return the string of binary representation of pi upto 32 decimal places.

Using the count() method associated with strings in python, we can do the counting of 1s by the python interpreter too instead of counting manually.

Calling binf(pi-int(pi//1),32).count('1') will directly give the answer as $14$ .

Prasun Biswas - 5 years, 2 months ago

Abdelhamid Saadi
Apr 8, 2016

A shorter solution in python

from math import pi

def solve(a, n):
    "Binary Pi, Anyone?"
    cnt  =  0
    for i in range(n):
        a *= 2
        if  a > 1:
            a -= 1
            cnt += 1 
    return cnt

print("Number of 1: ", solve(pi -3, 32))

Hasmik Garyaka
Oct 19, 2017

Use windows calc, calculate pi 2 *32 and click the bin button. 1100100100001111110110101010001000

Binary Pi, Anyone?

3 solutions

0 pending reports