numbers of digits vs powers of 2

numdigit_pwr2.py

"""
numbers of digits vs powers of 2
--------------------------------

plot (and print) in jupyter number of digits used by every power of 2 twom from 0 to 128, e.g.:
2^16 = 65536 (5 digits)

it is useful when converting binary to BCD (Binary Coded Decimal), often used in FPGA/ASIC
(using double-dabble algorithm) development, to convert a number into a human readable format, e.g.:

1. show in a 7-segment display
2. send via uart
3. print on a terminal, etc.

Given a number of digits, mutiply it by four to get the number of bits needed to represent it.
"""

from matplotlib import pyplot as plt

x = []
s = []

for i in range(0,129):
    x.append(2**i)
    s.append(len(str(x[i])))
    #print(i, x[i],s[i])

%matplotlib inline

xaxis = s
yaxis = range(0,129)
fig = plt.figure()
ax = fig.add_axes([0,0,2, 1])
ax.plot(xaxis,yaxis)
ax.set_title("number of digits base on powers of two")
ax.set_xlabel('digits')
ax.set_ylabel('powers of 2')