Suppose you want to print 768345 in base 10, one digit at a time.

STAGE 1:  Print them right-to-left (not sufficient for HW02)

Calc remainder:   768345 % 10 = 5    This is the 1's place digit, aka the 10⁰ place.

Calc quotient:    768345 / 10 = 76834

Calc remainder:   76834       % 10 = 4  This is the 10's place digit, aka the 10¹ place.
                  768345 / 10 % 10 = 4  ... because 76834 = 768345 / 10

Calc quotient:    76834 / 10 = 7683

Calc remainder:   7683         % 10 = 3    This is the 100's place digit, aka the 10² place.
                  768345 / 10² % 10  … because 7683 = 768345 / 10 / 10 = 768345 / 10².

Calc quotient:    7683 / 10 = 768

Calc remainder:   768 % 10 = 8       This is the 1000's place digit, aka the 10³ place.
                  768345 / 10³ % 10 … because 768 = 768345 / 10 / 10 / 10 = 768345 / 10³

Calc quotient:    768 / 10 = 76

Calc remainder:   76 % 10 = 6        This is the 10,000s place digit, aka the 10⁴ place.
                  768345 / 10⁴ % 10 … because 76 = 768345 / 10 / 10 / 10 / 10 = 768345 / 10⁴

Calc quotient:    76 / 10 = 7

Calc remainder:   7 % 10 = 7         This is the 100,000s place digit, aka the 10⁵ place.
                  768345 / 10⁵ % 10 … because 7 = 768345 / 10 / 10 / 10 / 10 / 10 = 768345 / 10⁵

7 / 10 = 0         We stop when the quotient is zero.


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HERE IS A POSSIBLE THOUGHT PROCESS

Question 1:  If you knew how many digits a number will require to represent, could you tell me the first digit?
    Ex:  If I give you 768336 and tell you that in base 10, it will require 6 digits, can you tell me that the first digit is '7'?
         First digit is 768336 ÷ 10⁵

Question 2:  If you knew how many digits a number will require to represent, could you tell me the second digit?
    Ex:  If I give you 768345 and tell you that in base 10, it will require 6 digits, can you tell me that the second digit is '6'?
         768345 / 10⁴ % 10

Question 3:  If you knew how many digits a number will require to represent, could you tell me the third digit?
    Ex:  If I give you 768345 and tell you that in base 10, it will require 6 digits, can you tell me that the second digit is '8'?
         768345 / 10³ % 10

Question 4:  If you knew how many digits a number will require to represent, could you tell me the i'th digit?
        len_digits is the number of digits needed to represent the number.
        digit_num is the digit (starting at 1); for the left-most digit, digit_num==1, for the next digit, digit_num==2, and so on.
        768345 / 10^(len_digits - digit_num) % 10

Question 5:  If I give you a number and a radix (base), can you calculate the number of digits needed to represent the number in that base?
    You don't have to answer in terms of a closed-form math expression (though you could if you wanted to).
    Ex: If n==768345 and radix==10, can you tell me that it requires 6 digits to express?


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Once you know the digit value for a particular place, how do you print the character?

Example:  If you wanted to print the number one-hundred sixty-three in base 16.

    Result:   a3
  16's place◀─┘└─▶1's place

Digit value for the 16's place is ten.

If digit_value is  0, we want to print '0'.
If digit_value is  1, we want to print '1'.   Remember:  '1' is '0' + 1
If digit_value is  2, we want to print '2'.   Remember:  '2' is '0' + 2
If digit_value is  3, we want to print '3'.
If digit_value is  4, we want to print '4'.
If digit_value is  5, we want to print '5'.
If digit_value is  6, we want to print '6'.
If digit_value is  7, we want to print '7'.
If digit_value is  8, we want to print '8'.
If digit_value is  9, we want to print '9'.
If digit_value is 10, we want to print 'a'.    Remember: 'a' is 'a' + 0
If digit_value is 11, we want to print 'b'.    Remember: 'b' is 'a' + 1
If digit_value is 12, we want to print 'c'.    Remember: 'c' is 'a' + 2
If digit_value is 13, we want to print 'd'.
If digit_value is 14, we want to print 'e'.
If digit_value is 15, we want to print 'f'.
If digit_value is 16, we want to print 'g'.
If digit_value is 17, we want to print 'h'.
If digit_value is 18, we want to print 'i'.
If digit_value is 19, we want to print 'j'.
If digit_value is 20, we want to print 'k'.
If digit_value is 21, we want to print 'l'.
If digit_value is 22, we want to print 'm'.
If digit_value is 23, we want to print 'n'.
If digit_value is 24, we want to print 'o'.
If digit_value is 25, we want to print 'p'.
If digit_value is 26, we want to print 'q'.
If digit_value is 27, we want to print 'r'.
If digit_value is 28, we want to print 's'.
If digit_value is 29, we want to print 't'.
If digit_value is 30, we want to print 'u'.
If digit_value is 31, we want to print 'v'.
If digit_value is 32, we want to print 'w'.
If digit_value is 33, we want to print 'x'.
If digit_value is 34, we want to print 'y'.
If digit_value is 35, we want to print 'z'.