Bits

A bit is one piece of information--also a BInary digiT. It's a yes or a no, an on or off, or a 1 or a 0. Many bits together can be used to store a lot of information, this is called a binary encoding.
Here is a graphic file using an ascii encoding for pbm (portable Bitmap Image)
P1
# CREATOR: GIMP PNM Filter Version 1.1
64 8
0011100100000000000000000000000001000001110000000000000000000000
0010010001000000000000000000000001000001001000000100000000000000
0010100101100111100001110011100111000001010010010110011101111000
0011010101000010000001110100101001000001101001010100111100100000
0010010101000001100010010100101001000001001001100100100000011000
0011110100110111100001110100100111000001111000100011011101111000
0000000000000000000000000000000000000000000001000000000000000000
0000000000000000000000000000000000000000000001000000000000000000
That file encodes this image: bitsNbytes2normal.png Here's a scaled version: bitsNbytes2.png

Bytes (8 bits)

Eight bits form a Byte. Below is a 64 byte version of the bitmap above.
9c 00 00 00 82 03 00 00
24 02 00 00 82 04 02 00
94 e6 e1 9c 83 92 e6 1e
ac 42 e0 52 82 a5 f2 04
a4 82 91 52 82 64 12 18
bc ec e1 92 83 47 ec 1e
00 00 00 00 00 20 00 00
00 00 00 00 00 20 00 00
Bytes along with a prefix are commonly used to describe the size of files. Kilobytes, megabytes, gigabytes, and terabytes are mean 1000 bytes, 1000000 bytes, 100000000 bytes, and 1000000000000 bytes. The first three are often shortened to just K, megs, and gigs.

To see this file you can use gimp (and probably photoshop).

Compression

Here is an example of 64x64 and a 128x128 pixel example for compression. The bigger image is four times the size which can be
Formats
Small zu64.png
Big zu128.png
pbm (plain text)
4.209 KB
16.563 KB
PNG (compressed)
345 B
607 B

Here's is the small pbm file (plain text)
P1
# CREATOR: GIMP PNM Filter Version 1.1
64 64
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000011111111111111111111111111111000000000000000000011111111100
0000011111111111111111111111111111100000000000000000011111111000
0000011111111111111111111111111111000000000000000000011111111100
0000011111111111111111111111111111100000000000000000011111111100
0000011111111111111111111111111111000000000000000000011111111100
0000011111111111111111111111111111100000000000000000011111111000
0000000001000100010001000111111111000000000000000000011111111100
0000000000000000000000000111111111000000000000000000011111111100
0000000000000000000000001111111111000000000000000000011111111100
0000000000000000000000011111111111000000000000000000011111111000
0000000000000000000000111111111111000000000000000000011111111100
0000000000000000000000111111110111100000000000000000011111111100
0000000000000000000001111111111111000000000000000000011111111100
0000000000000000000011111111111111000000000000000000011111111000
0000000000000000000111111110111111000000000000000000011111111100
0000000000000000001111111111111111100000000000000000011111111100
0000000000000000001111111111111111000000000000000000011111111100
0000000000000000011111111011111111000000000000000000011111111000
0000000000000000111111111011111111000000000000000000011111111100
0000000000000001111111110111111111100000000000000000011111111100
0000000000000011111111100111111111000000000000000000011111111100
0000000000000011111111000011111111000000000000000000011111111000
0000000000001111111110000111111111000000000000000000011111111100
0000000000001111111110000011111111100000000000000000011111111100
0000000000011111111000000111111111000000000000000000011111111100
0000000000111111111000000011111111000000000000000000011111111000
0000000000111111110000000111111111000000000000000000011111111100
0000000001111111100000000011111111100000000000000000111111111100
0000000011111111100000000111111111000000000000000000111111111000
0000000111111111000000000011111111100000000000000000111111111000
0000001111111110000000000011111111100000000000000000111111111000
0000011111111100000000000011111111111000000000000001111111111000
0000011111111000000000000001111111111100000000000111111111110000
0000111111111000000000000001111111111111000000111111111111110000
0001111111110010010010010101011111011111111111111111111111100000
0001111111111111111111111111111111111111111111111111111111000000
0001111111111111111111111111111111111111111111111111111111000000
0001111111111111111111111111111111101111111111111111111100000000
0001111111111111111111111111111111111111111111111111110000000000
0011111111111111111111111111111111111111111111111111000000000000
0001111111111111111111111111111111110011111111111100000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000

(note to self--for 64 chars per line)
sed 's/.\{64\}/&\
/g'