Question

Assume that base64 Transfer Encoding (or Radix-64 Encoding) is used by an MIME application to encode arbitrary binary input into printable ASCII characters. If an ASCII string output of four printable characters, e5Gy is generated by this MIME application, then the corresponding 24-bit raw input should be

Answer 1

As we know base10 is the decimal representation we use to write numbers. It provides us with the 10 printable ASCII characters 0-9 to represent numbers.

Similarly base2 is the binary representation which provides us with 2 printable ASCII characters 0-1 to represent numbers.

On the similar lines base64 provides us with a set of 64 printable ASCII characters to represent any information and these characters are as below:

A-Z

a-z

0-9

+

/

Below is the detailed table showing the characters and their corresponding position (ordering) in base64 encoding system.

Index	Value	Index	Value	Index	Value	Index	Value
0	A	16	Q	32	g	48	w
1	B	17	R	33	h	49	x
2	C	18	S	34	i	50	y
3	D	19	T	35	j	51	z
4	E	20	U	36	k	52	0
5	F	21	V	37	l	53	1
6	G	22	W	38	m	54	2
7	H	23	X	39	n	55	3
8	I	24	Y	40	o	56	4
9	J	25	Z	41	p	57	5
10	K	26	a	42	q	58	6
11	L	27	b	43	r	59	7
12	M	28	c	44	s	60	8
13	N	29	d	45	t	61	9
14	O	30	e	46	u	62	+
15	P	31	f	47	v	63	/

Also as we could represent 0-63 values using just 6 bits:

64 = 2⁶

To encode the given base64 string (e5Gy) into its bit representation we just need to perform the below steps for every character in the string:

1) Pick i^th character where i is 1 to string length

2) Locate this character in the Value column in above table

3) Note its Index

4) Convert this Index into its bit representation

5) Print the bit representation

On applying the above steps on each given base64 string character (e5Gy):

e = 30 = 011110

5 = 57 = 111001

G = 6 = 000110

y = 50 = 110010

So the conversion from base64 to bits is:

011110 111001 000110 110010