Digital Electronics

Chapter 1

Binary Systems

Digital Electronics Galore!

•Digital Cameras

•Digital Versatile Disks (DVD)

•Digital Computers

•Digital Televisions

•Digital Telephones

•Digital Birthday Cards

Binary Numbers

103 102 101 100

7 5 8 3

1 1 0 1

23 22 21 20

Decimal

Binary

Binary Drill

1101 = ?

1001 = ?

1000 = ?

0101 = ?

1010 = ?

Binary Drill … Solutions

1101 = 13

1001 = 9

1000 = 8

0101 = 5

1010 = 10

Hexadecimal (Base 16)

163 162 161 160

So 3816 = what in decimal?

Hexadecimal Solution

3816 = 5610

Decimal - Hexadecimal

0 through 9 = 0 through 9

10 = A

11 = B

12 = C

13 = D

14 = E

15 = F

16 = 10

17 = 11

18 = 12

Hexadecimal Drill

2B7 = what in decimal?

Hint: Think … 163 162 161 160

Hexadecimal Drill … Solution

2B7 = 256 x 2 + 16 x 11 + 7

Hint: Think … 163 162 161 160

2B716 = 69510

Hexadecimal To Binary

2B7 = what in binary?

Hint

Secret Recipe: Convert digit by digit!!!

Hex2Bin … Solution

2B7 = what in binary?

Secret Recipe: Convert digit by digit!!!

2 B 716 = 0010 1011 0111

Octal (Base 8)

83 82 81 80

So 658 = what in decimal?

Octal Solution

658 = 5310

Decimal - Octal

0 = 0

1 = 1

2 = 2

3 = 3

4 = 4

5 = 5

6 = 6

7 = 7

8 = 10

9 = 11

10 = 12

Octal Drill

2178 = what in decimal?

Hint: Think … 83 82 81 80

Octal Drill … Solution

2178 = 64 x 2 + 8 x 1 + 7

2178 = 14310

Hint: Think … 83 82 81 80

Octal To Binary

2178 = what in binary?

Hint : Groups of 3

Secret Recipe: Convert digit by digit!!!

Oct2Bin … Solution

217 = what in binary?

Secret Recipe: Convert digit by digit!!!

2 1 78 = 010 001 111

Fractions in Binary

21.75 = what in binary?

2 1.7510 = 10101. 11

23 22 21 20 . 2-1 2-2 2-3

Fractions … Drill

41.6875 = what in binary?

23 22 21 20 . 2-1 2-2 2-3

Fractions … Drill

41.687510 = 101001.1011

23 22 21 20 . 2-1 2-2 2-3

Complements

1’s complement is formed by inverting the digits

1’s complement of 10010001 = 01101110

2’s complement is formed by adding 1 to the 1’s complement

2’s complement of 10010001 = 01101111

Negative (signed) Numbers

2’s complement is used to represent a negative number

Example: 117 - 102

115 = 01110011 and 102 = 01100110

So -102 = 10011010

So 115 = 01110011

-102 = 10011010

13 = 00001101

BCD (Binary Coded Decimal)

Example

87510 = 1000 0111 0101

Note that each digit is coded individually. Do not confuse this with pure binary!

ASCII Character Codes

CAPS: A = 4116 = 1000001

G = 4716 = 1000010

Z = 5A16 = 1011010

lower case a = 6116 = 1100001

h = 6816 = 0111000

z = 7A16 = 1111010

digits 0 -9 4 = 3416 = 0110100

8 = 3816 = 0111000

Error Detection and Parity

Parity bit is an extra bit added to make the total number of 1’s even or odd depending on the protocol agreed upon

A with even parity = 01000001

A with odd parity = 11000001

Parity bit helps in detecting errors during transmission.

Binary Logic

AND means ALL conditions must be TRUE for the outcome to be true. For instance, you must study AND take the test in order to pass this class.

OR means AT LEAST ONE condition must be true for the outcome to be true. For instance, you can walk, ride the bike, or drive to get to school.

Logic Gates

AND OR

x y x y x y x+y

0 0 0 0 0 0

0 1 0 0 1 1

1 0 0 1 0 1

1 1 1 1 1 1

Digital Logic Gates

AND OR NOT

Timing Diagrams

That’s All Folks!