Data Representation

Binary Representation

Everything in the computer is represented using a very simple binary coding scheme where the only symbols used are 0 and 1.

• Magnetic disks: magnetic material can be polarized to one and two extremes (“north” or “south”) to represent a 0 or a 1.
• Memory: each bit can be thought of as an electronic switch that is either off or on representing a 0 or a 1, or, depending on how the memory is made, as collections of electrons. (In old days, memory literally was tiny circular magnets, but no longer.)
• CDs/DVDs: the surface consists of smooth areas and pits representing 0’s and 1’s respectively.
• Bus (wire): voltage or current

What can be represented by bits?

• a bit (short for “binary digit”) is the fundamental data component: either a 1 or a 0
• 8 bits** is called a byte, A byte can represent:
  • 256 different numbers
  • 256 different characters from your keyboard (Programming languages typically use 2 byte to represent a character)
  • 256 different shades of gray in a black and white image
  • 256 colors or shades of color in a color image
  • 256 frequencies or tones to be played through a speaker
  • 256 of anything that can be represented as discrete entities
• the max value for $n$ bits is $2^{n-1} - 1$, whereas the min value is $-2^n$.

Number System

Base 10	Base 2	Base 8	Base 16
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F

Signed Numbers

Signed Magnitude

• the left-most bit in the binary number is the sign
  • 0 is positive
  • 1 is negative
• $00000011_2$ is $+3_{10}$
• $10000011_2$ is $-3_{10}$

Two’s Complement

take opposite of each bit, then add one

Characters

ASCII

American Standard Code for Information Interchange

• A-Z: 65-90
• a-z: 97-122
• 0-9: 48-57

Unicode

addition to ASCII that can represent more characters, covers lots of emojis and most existing languages.

More Information