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Software must convert instructions given

by the user into a form so that thehardware can understand.

The communication between hardwareand software is reduced to a simple

“YES” or “NO” / “ON” or “OFF”. 

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In the early days they attempted to store

a charge in a vacuum tube, which issimilar to a light bulb.

Each digit in our number system (0-9)was stored with increasing degrees ofcharge.

But this method was inefficient andsometimes inaccurate.

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145610

1x6

10x5100x4

1000x1

1000 400 50 6++ +

145610 

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1 = 100

10 = 101

100 = 102

1000 = 103 

10,000 = 104

…. 

………….. 

………………… 

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Exercise

1. 125

2. 45

3. 6698

4. 4511

5. 25878

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The binary number system works in the exactsame way as the decimal system, exceptthat it contains only 2 digits, 1 and 0.

In order to count further, we need to add asecond column worth twice the value of thecolumn before…. 

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1 –  20 - 1x1 - 0001

2 –  21 - 1x0 + 2x1 - 0010

4 –  22 - 1x0 + 2x0 + 4x1 - 0100

8 –  23 - 1x0 + 2x0 + 4x0 + 8x1 - 1000

16 –  24 - 1x0 + 2x0 + 4x0 + 8x0 + 16x1 - 1 0000

32 –  25 - 1x0 + 2x0 + 4x0 + 8x0 + 16x0 + 32x1 - 10 0000

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Decimal to Binary

1. 22. 8

3. 15

4. 49

5. 102

6. 256

Binary to Decimal1. 00101

2. 000111

3. 110001

4. 1101001

5. 0001001

6. 1101011

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A 1 or 0 is called a bit or Binary Digit.

Grouping is often done in group of 8 bits.This is called a byte.

When text is stored, every letter orcharacter is first converted to a code using only zeros and ones.

The most common coding method fortext is ASCII (American Standard forInformation Interchange)

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With 8 bits in a byte, we can represent

256 values ranging from 0 – 

 255.

Numeric - 10

Alphabetic - Upper –  26- Lower - 26

Punctuation - 15

Arithmetic - 7 Other - 12

96

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Kilo - 210 - 1024 --> 103

Mega - 220 - 1, 048, 576 --> 106

Giga - 230 - 1, 073, 741, 824 --> 109

Tera – 

 2

40

Peta - 250 

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How many Megabytes?

1. 205 Kb

2. 30152 bytes

3. 4 GB

4. 6430 Kb

How many Gigabytes?1. 2434 MB

2. 248 TB

File has 1024 bytes. How many Kb are there?

File has 8192 bytes. How many Kb are there?

File has 205 Kb. How many MB are there?

File has 642 MB. How many GB are there?