Step-by-step binary, dex, and decimal conversion

binary_conversion_steps.py

# This is a learning tool to illustrate the steps of converting from 
# one number system to another. 

# dec2hex(int) Convert a decimal number to hex step-by-step.
# dec2bin(int) Convert binary number to decimal step-by-step.
# bin2dec(string) Convert a binary fraction to a decimal fraction. 12 decimal places.
# bin2float(string) Convert a binary fraction to a decimal fraction with scientific notation.
# float2bin(float) Convert a decimal fraction to a binary fraction.

def low_scientific(n, pnt=True):
    '''
    Convert numbers less than one to scientific notation. 
    Returns the normalized float and decimal exponent. 
    '''
    exp = 0
    while n < 1:
        n *= 10
        exp += 1
    if pnt:
        print("%.5f x 10^-%d" % (n, exp))
    return n, exp

def dec2hex(n):
    '''
    Convert a decimal integer to hex step-by-step.
    '''
    print("==========")
    num = []
    letters = {10: "A", 11: "B", 12: "C", 13: "D", 14: "E", 15: "F"}
    r = 0;
    while (n != 0):
        r = n % 16
        if (r<10):
            num.append(r)
            print("%d %% 16 = %d" % (n, r) )
        else:
            num.append(letters[r])
            print("%d %% 16 = %d (%s)" % (n, r, letters[r]) )
        print("%d / 16 = %d" % (n, int(n/16)))
        n = int(n / 16)
        print()
    print(' '.join(map(str, num[::-1])))
    print("==========")


def dec2bin(n):
    '''
    Convert decimal integer to binary step by step.
    '''
    print("==========")
    num = []
    r = 0;
    while (n != 0):
        r = n % 2
        num.append(r)
        print("%d %% 2 = %d" % (n, r) )
        print("%d / 2 = %d" % (n, int(n/2)))
        n = int(n / 2)
        print()
    print(' '.join(map(str, num[::-1])))
    print("==========")


def bin2dec(binary):
    '''
    Convert binary integer to decimal step-by-step.
    '''
    sum = 0
    n = 0
    for digit in binary[::-1]:
        if (digit == '1'):
            print("1*2^%d or %d" % (n, 2**n))
            sum += 2**n
        else:
            print("0*2^%d or 0" % n)
        n+=1
        print()
    print("Total: %d" % sum)


def bin2float(fraction, start=1):
    '''
    Convert a binary fraction to a decimal fraction. Simply prints 12 decimals.
    Input is a string with the binary values to the right of the decimal. 
    Fraction is a string of binary digits, start is the binary exponent. 
    Pass a positive exponent even though it's negative. 
    '''
    print("==========")
    print("Binary fraction: %s" % fraction)
    n = start
    sum = 0.0
    for digit in fraction:
        if (digit == "1"):
            print("2^-%d = %.12f" % (n, (2**-n)))
            sum += 2**-n
            print("Subtotal = %.12f" % sum)
        else:
            print("Passing 0 digit at 2^-%d" % n)
        n += 1
    print()

    print("Total: %.12f" % sum)
    print("==========")


def bin2longfloat(fraction, start=1):
    '''
    Convert a binary fraction to a decimal fraction with scientific notation.
    Input is a string with the binary values to the right of the decimal. 
    This one works with very small numbers. 
    Fraction is a string of binary digits, start is the binary exponent. 
    Pass a positive exponent even though it's negative. 
    '''
    print("==========")
    print("Binary fraction: %s, start at 2^%d" % (fraction, start))
    print()
    n = start
    sum = 0.0
    for digit in fraction:
        if (digit == "1"):
            temp_val, temp_exp = low_scientific(2**-n, pnt=False)
            print("Add 2^-%d = %.8f x 10^-%d" % (n, temp_val, temp_exp))
            sum += 2**-n
            print("Subtotal = %.8f x 10^-%d" % (low_scientific(sum, pnt=False)))
        else:
            print("Passing 0 digit at 2^-%d" % n)
        n += 1
        print()
    print("Total: %.50f" % sum)

    print("Total = %.8f x 10^-%d" % (low_scientific(sum, pnt=False)))

    print("==========")


def float2bin(fraction, limit=0):
    '''
    Convert a decimal fraction to a binary fraction.
    Input is a decimal number between 0 and 1. Basically the right side of the decimal point. 
    '''
    print("==========")
    num = []
    for i in range(1, limit+6):
        print("%f * 2 = %f" % (fraction, fraction * 2))
        fraction *= 2
        if (fraction >= 1):
            print("Append '1' to binary, subtract 1")
            num.append(1)
            fraction -= 1
        else:
            print("Append '0' to binary")
            num.append(0)
        if (i == limit):
            num.append(" Trailing: ")
        print()
    print(''.join(map(str, num)))
    print("==========")

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