Computer Hardware

1
Computer Hardware

• Introduction to Computer Hardware
• Binary Arithmetic
• Boolean Logic

2
Digital Hardware States

• Voltage or current can be off or on state
• Value can be interpreted as
• Off On
• 0 1 ? Binary Arithmetic
• false true ? Boolean Logic
• Now lets look at each of these in turn

3
Decimal Arithmetic

• Counting in decimal with digits 0 through 9
• 000
• 001
• 009
• 010 (carry)
• 099
• 100 (carry)

4
Binary Arithmetic

• Counting in binary with digits 0 through 1
• 0000 decimal 0
• 0001 decimal 1
• 0010 decimal 2 (carry)
• 0011 decimal 3
• 0100 decimal 4 (carry)
• 0101 decimal 5
• 0110 decimal 6 (carry)
• 0111 decimal 7
• 1000 decimal 8 (carry)

5
Decimal Arithmetic

• Value of decimal digits in each position
• Powers of 10 ? 1, 10, 100, 1000, 10000,

10 4
10 3
10 2
10 1
10 0 1
1
0
1
0
1
Decimal 10101 Decimal 10000 100 1
6
Binary Arithmetic

• Value of binary digits in each position
• Powers of 2 ? 1, 2, 4, 8, 16,

2 4 16
2 3 8
2 2 4
2 1 2
2 0 1
1
0
1
0
1
Binary 10101 Decimal 21 ( 16 0 4 0 1)
7
Binary Arithmetic

• How to Add in Binary
• Addition Table
• Examples

0
1
0
0
1
0 carry 1
1
1
0
0
1
01
11
3
0

1

0

01

01

1

10
100
4
0
1
1
8
Binary Arithmetic

• How to Multiply in Binary
• Multiplication Table
• Examples

0
1
0
0
0
1
0
1
0
0
1
1
10
2
0
x
1
x
0
x
1
x
11
x
3
x
1
10
6
0
0
0
10

110
9
Boolean Logic

• How to AND in Binary
• AND Table
• Examples

0
1
0
0
0
1
0
1
Double Locked Door Have Key1 1 AND Have Key2
1 ? Can Get In 1 Have Key1 1 AND Have Key2
0 ? Can Get In 0 Have Key1 0 AND Have Key2
1 ? Can Get In 0 Have Key1 0 AND Have Key2
0 ? Can Get In 0
10
Boolean Logic

• How to OR in Binary
• OR Table
• Example

0
1
0
0
1
1
1
1
Door Open 1 OR Have Key 1 ? Can Get In
1 Door Open 0 OR Have Key 1 ? Can Get In
1 Door Open 1 OR Have Key 0 ? Can Get In
1 Door Open 0 OR Have Key 0 ? Can Get In 0
11
Boolean Logic

• How to Exclusive OR in Binary
• XOR Table
• Example

0
1
0
0
1
1
1
0
Dual Light Switch Control Switch1 0 XOR
Switch2 0 ? Light On 0 Switch1 0 XOR
Switch2 1 ? Light On 1 Switch1 1 XOR
Switch2 0 ? Light On 1 Switch1 1 XOR
Switch2 1 ? Light On 0
12
Boolean Logic

• How to NOT in Binary
• NOT Table
• Examples

0
1
1
0
Door Locked 1 ? Can Get In 0 Door Locked 0
? Can Get in 1
13
Review of First Generation

• Electromechanical Relays - Boolean AND

Voltage (Battery)
Relay 3 Relay 1 AND Relay 2
Relay 1
Relay 2
Electromagnet
Electromagnet
Electromagnet
Ground (Battery)
14
Review of First Generation

• Electromechanical Relays - Boolean OR

Voltage (Battery)
Relay 3 Relay 1 OR Relay 2
Relay 1
Relay 2
Electromagnet
Electromagnet
Electromagnet
Ground (Battery)
15
Using Logg-O at AE Online Site

• Allows you to connect switches, logic gates, and
  lights to see the effect of Boolean logic
• AND
• OR XOR
• NOT

16
Logg-O

• Lets Try it Now
• Link to AE Online Site from Syllabus Page
• Select Module 7
• Select Lab 7.1
• Tools
• Hand
• Connect
• Run
• Scissors