1. How Computers Store Data
All data in a computer is stored in sequences of 0s and 1s
Byte: just enough memory to store letter or small number
Divided into eight bits
Bit: electrical component that can hold positive or negative charge, like on/off switch
The on/off pattern of bits in a byte represents data stored in the byte

4. Storing Numbers Bit represents two values, 0 and 1
Computers use binary numbering system
Position of digit j is assigned the value 2j-1
To determine value of binary number sum position values of the 1s
Byte size limits are 0 and 255
0 = all bits off; 255 = all bits on
To store larger number, use several bytes

6. How to Convert Decimal to Binary
Convert 37 to binary
128 doesn’t fit into 37 b7=0
64 doesn’t fit into 37 b6=0
32 fits into 37 b5=1
37 – 32 = 5, continue the process with 5
16 doesn’t fit into 5 b4=0
8 doesn’t fit into 5 b3=0
4 does fit into 5 b2=1
5-4=1, continue process with 1
2 doesn’t fit into 1 b1=0
1 does fit into 1 b0=1
Final answer:

7. Convert 69 to Binary 128 64 32 16 8 4 2 1 128 doesn’t fit into 69 b7=0
128 doesn’t fit into b7=0
64 does fit into b6=1
Subtract: 69-64=5
Continue process with 5
32 doesn’t fit into b5=0
16 doesn’t fit into b4=0
8 doesn’t fit into b3=0
4 does fit into b2=1
Subtract: = 1
Continue the process with 1
2 doesn’t fit into b1=0
1 fits into b0=1

8. Convert 37 to Binary - Second Method
Divide by 2 and store the remainder
37/2= b0=1
18/2 = b1=0
9/2= b2=1
4/2= b3=0
2/2= b4=0
1/2= b5=1
Write remainders from bottom up and pad with leading 0’s to fill all 8 bits

9. Convert 259 to binary 259/2 = 129 b0=1 129/2 = 64 b1=1 64/2 = 32 b2=0
2 bytes are needed to store this number

11. Storing Characters
Data stored in computer must be stored as binary number
Characters are converted to numeric code, numeric code stored in memory
Most important coding scheme is ASCII
ASCII is limited: defines codes for only 128 characters
Unicode coding scheme becoming standard
Compatible with ASCII
Can represent characters for other languages

13. Advanced Number Storage
To store negative numbers and real numbers, computers use binary numbering and encoding schemes
Negative numbers encoded using two’s complement
Real numbers encoded using floating-point notation

14. Other Types of Data
Digital: describes any device that stores data as binary numbers
Digital images are composed of pixels
To store images, each pixel is converted to a binary number representing the pixel’s color
Digital music is composed of sections called samples
To store music, each sample is converted to a binary number