Bits and Bytes

Behind the scenes in your computer

All computer storage is organized into bytes

• Think of each byte as a little storage bin• Each byte is made up of 8 bits• Each bit is an electronic circuit that is either on

or off (off = 0, on = 1)• A specific sequence of 0’s and 1’s in a byte is

called a bit pattern

So, how many bytes are in your computer?Common Prefixes

Kilo 103 1,000 Thousand

Mega 106 1,000,000 Million

Giga 109 1,000,000,000 Billion

Tera 1012 1,000,000,000,000 Trillion

Typical Capacities:

RAM: 1, 2, 4, 6 or 8 GB

Diskette: 1.44 MBFlash drive: 2, 4, 8, 16, 32, 64, 128 GBCD: 800 MBDVD: 4.7 GBHard Drive: 500 GB – 2 TB

Converting Between UnitsTo Convert …

From To Action

KB Bytes Multiply by 1,000 (move decimal point 3 places right)

MB Bytes Multiply by 1,000,000 (move decimal point 6 places right)

GB Bytes Multiply by 1,000,000,000 (move decimal point 9 places right)

Bytes KB Divide by 1,000 (move decimal point 3 places left)

Bytes MB Divide by 1,000,000 (move decimal point 6 places left)

Bytes GB Divide by 1,000,000,000 (move decimal point 9 places left)

Example 1: 5200 KB = ? MB

5200 × 1000 = 5,200,000 bytes5,200,000 /1,000,000 = 5.2 MB

Example 2: 7.5 GB = ? KB

7.5 × 1,000,000,000 = 7,500,000,000 bytes7,500,000,000 / 1000 = 7,500,000 KB

You Try:

3.2 MB = ? Bytes

6.4 GB = ? MB

57,000 Bytes = ? KB

25,000 KB = ? MB

What kinds of information do you store on your computer?

• numerical values (binary number system)• text/character data (ASCII or Unicode)• program instructions (machine language)• images (jpg, gif, tiff, bmp, wmf, etc.)• video (mp4, mov, avi, wmv, etc.)• music (mp3, wav, wma, au, etc.)

“Kathy Ames” is text

01001011011000010111010001101000011110010010000000100001011011010110010101010011

It would be stored like this using ASCII codes

Numerical values needed for arithmetic are stored using a different scheme

The numerical value 40 would be stored like this using the binary number system.

00101000

(note that “bit” stands for “binary digit”)

How do binary numbers work?Decimal Number System Binary Number System

Base 10 Base 2

10 digits (0,1,2,3,4,5,6,7,8,9) 2 digits (0,1)

Positional values based on powers of 10 Positional values based on powers of 2

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number

8-bit binary number

Converting from Binary to Decimal

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 0 1 1 0 1 0 1 0

What is the decimal value of the bit pattern 01101010 ?

Simple! Just add up the positional values where the 1’s appear: 64 + 32 + 8 + 2 = 106

So, we say that 011010102 = 106 decimal

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number

How can we represent the decimal value 151 in binary?

Simple! Just think about money and consider positional values as bills and 151 “dollars” as the amount we must make.

Then “count change” from largest “denomination” to smallest until total value of change is accumulated.

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1

How can we represent the decimal value 151 in binary?

Running Total: 128

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1 0

How can we represent the decimal value 151 in binary?

Running Total: 128

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1 0 0

How can we represent the decimal value 151 in binary?

Running Total: 128

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1 0 0 1

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 = 144

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1 0 0 1 0

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 = 144

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1 0 0 1 0 1

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 + 4 = 148

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1 0 0 1 0 1 1

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 + 4 + 2 = 150

Converting from Decimal to Binary

Positional Values

128 64 32 16 8 4 2 1

27 26 25 24 23 22 21 20

Binary Number 1 0 0 1 0 1 1 1

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 + 4 + 2 + 1 = 151

So, 151 decimal = 100101112

So What is Hexadecimal?(often called “hex”)

• A base 16 number system• 16 possible digits:

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F• Positional values are powers of 16• Mainly used is as “short hand” for binary• 1 hex digit = 4 binary digits

Hex Digits

Dec Value 0 1 2 3 4 5 6 7Hex Digit 0 1 2 3 4 5 6 74-bit binary 0000 0001 0010 0011 0100 0101 0110 0111

Dec Value 8 9 10 11 12 13 14 15Hex Digit 8 9 A B C D E F4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111

Converting from Hex to Decimal

Positional Values

16 1

161 160

Hex Number 3 B

What is the decimal value of hex 3B?

Simple! 3 × 16 + B × 1 = 3 × 16 + 11 × 1 = 48 + 11 = 59

So, we say that 3B hex = 59 decimal

Converting from Hex to Decimal

Positional Values

16 1

161 160

Hex Number E 4

What is the decimal value of hex E4?

Simple! E × 16 + 4 × 1 = 14 × 16 + 4 × 1 = 224 + 4 = 228

So, we say that E4 hex = 228 decimal

Let’s take another look at Hex 3BDec Value 0 1 2 3 4 5 6 7Hex Digit 0 1 2 3 4 5 6 74-bit binary 0000 0001 0010 0011 0100 0101 0110 0111

Dec Value 8 9 10 11 12 13 14 15Hex Digit 8 9 A B C D E F4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111

First Digit Second Digit

3 B

0011 1011

So Hex 3B = 00111011 Binary

(And note that 00111011 Binary= 32 + 16 + 8 + 2 + 1 = 59 Decimal)

Let’s take another look at Hex E4Dec Value 0 1 2 3 4 5 6 7Hex Digit 0 1 2 3 4 5 6 74-bit binary 0000 0001 0010 0011 0100 0101 0110 0111

Dec Value 8 9 10 11 12 13 14 15Hex Digit 8 9 A B C D E F4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111

First Digit Second Digit

E 4

1110 0100

So Hex E4 = 11100100 Binary

(And note that 11100100 Binary= 128 + 64 + 32 + 4 = 228 Decimal)

What about converting Binary 10100010 to Hex?

Dec Value 0 1 2 3 4 5 6 7Hex Digit 0 1 2 3 4 5 6 74-bit binary 0000 0001 0010 0011 0100 0101 0110 0111

Dec Value 8 9 10 11 12 13 14 15Hex Digit 8 9 A B C D E F4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111

First Digit Second Digit

1010 0010

What about converting Binary 10100010 to Hex?

Dec Value 0 1 2 3 4 5 6 7Hex Digit 0 1 2 3 4 5 6 74-bit binary 0000 0001 0010 0011 0100 0101 0110 0111

Dec Value 8 9 10 11 12 13 14 15Hex Digit 8 9 A B C D E F4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111

First Digit Second Digit

1010 0010

A 2So 10100010 Binary = A2 Hex

Verify thatBinary 10100010 and Hex A2

have the same Decimal values

Binary 10100010 = 128 + 32 + 2 = 162

Hex A2 = A × 16 + 2 × 1 = 10 × 16 + 2 × 1 = 160 + 2 = 162

You try:

Convert 210 Decimal to:Binary:Hex:

Convert 2D Hex to:Binary:Decimal:

Convert 10001100 Binary to:Hex:Decimal: