Bits and bytes
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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)

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Bits and Bytes

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Bits and bytes

Bits and Bytes

Behind the scenes in your computer


All computer storage is organized into bytes

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

So, how many bytes are in your computer?

Typical Capacities:

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

Diskette: 1.44 MB

Flash drive: 2, 4, 8, 16, 32, 64, 128 GB

CD: 800 MB

DVD: 4.7 GB

Hard Drive: 500 GB – 2 TB


Converting between units

Converting Between Units

Example 2: 7.5 GB = ? KB

7.5 × 1,000,000,000 = 7,500,000,000 bytes

7,500,000,000 / 1000 = 7,500,000 KB

Example 1: 5200 KB = ? MB

5200 × 1000 = 5,200,000 bytes

5,200,000 /1,000,000 = 5.2 MB


You try

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

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

“Kathy Ames” is text

It would be stored like this using ASCII codes


Numerical values needed for arithmetic are stored using a different scheme

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.

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


How do binary numbers work

How do binary numbers work?

8-bit binary number


Converting from binary to decimal

Converting from Binary to Decimal

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

Converting from Decimal to Binary

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 binary1

Converting from Decimal to Binary

How can we represent the decimal value 151 in binary?

Running Total: 128


Converting from decimal to binary2

Converting from Decimal to Binary

How can we represent the decimal value 151 in binary?

Running Total: 128


Converting from decimal to binary3

Converting from Decimal to Binary

How can we represent the decimal value 151 in binary?

Running Total: 128


Converting from decimal to binary4

Converting from Decimal to Binary

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 = 144


Converting from decimal to binary5

Converting from Decimal to Binary

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 = 144


Converting from decimal to binary6

Converting from Decimal to Binary

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 + 4 = 148


Converting from decimal to binary7

Converting from Decimal to Binary

How can we represent the decimal value 151 in binary?

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


Converting from decimal to binary8

Converting from Decimal to Binary

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

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

Hex Digits


Converting from hex to decimal

Converting from Hex to Decimal

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 decimal1

Converting from Hex to Decimal

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 3b

Let’s take another look at Hex 3B

So Hex 3B = 00111011 Binary

(And note that 00111011 Binary

= 32 + 16 + 8 + 2 + 1 = 59 Decimal)


Let s take another look at hex e4

Let’s take another look at Hex E4

So Hex E4 = 11100100 Binary

(And note that 11100100 Binary

= 128 + 64 + 32 + 4 = 228 Decimal)


What about converting binary 10100010 to hex

What about converting Binary 10100010 to Hex?


What about converting binary 10100010 to hex1

What about converting Binary 10100010 to Hex?

So 10100010 Binary = A2 Hex


Verify that binary 10100010 and hex a2 have the same decimal values

Verify thatBinary 10100010 and Hex A2have the same Decimal values

Binary 10100010 = 128 + 32 + 2 = 162

Hex A2 = A × 16 + 2 × 1

= 10 × 16 + 2 × 1 = 160 + 2 = 162


You try1

You try:

Convert 210 Decimal to:

Binary:

Hex:

Convert 2D Hex to:

Binary:

Decimal:

Convert 10001100 Binary to:

Hex:

Decimal:


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