Binary is as easy as 1, 10, 11

Definition

Binary - In mathematics and digital electronics, a binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one).- https://en.wikipedia.org/wiki/Binary_number

Notes

• BASE 2 Counting method only uses 0 and 1
• One binary digit is called a bit
• Two digits are called a crumb, four digits are called a nibble, and eight digits are called a byte
• Lower Case letters start with 011xxxxx
• Upper Case letters start with 010xxxxx
• When counting, range 0-1, carry the 1 (i.e. 00000000, 00000001, 00000010, 00000011, 00000100, 00000101, 00000110, 00000111, 00001000, 00001001, 00001010 ...)
• 1+1=10

Converting binary (BASE 2) to decimal (BASE 10)

A byte can be represented as:

n·2^7 | n·2^6 | n·2^5 | n·2^4 | n·2^3 | n·2^2 | n·2^1 | n·2^0

OR

n·128 | n·64 | n·32 | n·16 | n·8 | n·4 | n·2 | n·1*

*Any nonzero number raised to the zero power is equal to one (i.e., n^0=1). This concludes that all nonzero numbers raised to the zero power are equivalent because they all equal 1. Note that it is any nonzero number, since 00 is undefined.

Conversion Examples

10 = 1·2^1 | 0·2^0 = 1·2 + 0·1 = 2
111 = 1·2^2 | 1·2^1 | 1·2^0 = 1·4 + 1·2 + 1·1 =7
1011 =  1·2^3 | 0·2^2 | 1·2^1 | 1·2^0 = 1·8 + 0 + 1·2 + 1 = 11

Converting binary (BASE 10) to decimal (BASE 2)

2^4 2^3 2^2 2^1 2^0

16 8 4 2 1

Use the value in the second row to count to the value--you can use each value no more than 1 time (since we count 0..1). For example, we want to convert 22 to binary. To do this we need:

(1 x 16) + (0x8) + (1x4) + (1x2) + (0x1)

10110 = 22

Letter to ASCII to Binary Character Table

Letter	ASCII Code	Binary	Letter	ASCII Code	Binary
a	097	01100001	A	065	01000001
b	098	01100010	B	066	01000010
c	099	01100011	C	067	01000011
d	100	01100100	D	068	01000100
e	101	01100101	E	069	01000101
f	102	01100110	F	070	01000110
g	103	01100111	G	071	01000111
h	104	01101000	H	072	01001000
i	105	01101001	I	073	01001001
j	106	01101010	J	074	01001010
k	107	01101011	K	075	01001011
l	108	01101100	L	076	01001100
m	109	01101101	M	077	01001101
n	110	01101110	N	078	01001110
o	111	01101111	O	079	01001111
p	112	01110000	P	080	01010000
q	113	01110001	Q	081	01010001
r	114	01110010	R	082	01010010
s	115	01110011	S	083	01010011
t	116	01110100	T	084	01010100
u	117	01110101	U	085	01010101
v	118	01110110	V	086	01010110
w	119	01110111	W	087	01010111
x	120	01111000	X	088	01011000
y	121	01111001	Y	089	01011001
z	122	01111010	Z	090	01011010

References 

• http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary
• https://www.mathsisfun.com/numbers/binary-count-fingers.html
• https://en.wikipedia.org/wiki/Binary_number