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Bits and Bytes

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Bits and Bytes

Behind the scenes in your computer

- 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

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

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

3.2 MB = ? Bytes

6.4 GB = ? MB

57,000 Bytes = ? KB

25,000 KB = ? MB

- 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.)

It would be stored like this using ASCII codes

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

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

8-bit binary number

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

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.

How can we represent the decimal value 151 in binary?

Running Total: 128

How can we represent the decimal value 151 in binary?

Running Total: 128

How can we represent the decimal value 151 in binary?

Running Total: 128

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 = 144

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 = 144

How can we represent the decimal value 151 in binary?

Running Total: 128 + 16 + 4 = 148

How can we represent the decimal value 151 in binary?

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

How can we represent the decimal value 151 in binary?

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

So, 151 decimal = 100101112

- 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

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

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

So Hex 3B = 00111011 Binary

(And note that 00111011 Binary

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

So Hex E4 = 11100100 Binary

(And note that 11100100 Binary

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

So 10100010 Binary = A2 Hex

Binary 10100010 = 128 + 32 + 2 = 162

Hex A2 = A × 16 + 2 × 1

= 10 × 16 + 2 × 1 = 160 + 2 = 162

Convert 210 Decimal to:

Binary:

Hex:

Convert 2D Hex to:

Binary:

Decimal:

Convert 10001100 Binary to:

Hex:

Decimal: