Digital Electronics

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Digital Electronics
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Chapter 1
Binary Systems
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Digital Electronics Galore!

• Digital Cameras

• Digital Versatile Disks (DVD)

• Digital Computers

• Digital Televisions

• Digital Telephones

• Digital Birthday Cards

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Binary Numbers
7 5 8 3
Decimal
103 102 101 100
1 1 0 1
Binary
23 22 21 20
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Binary Drill
1101 ?
1001 ?
1010 ?
1000 ?
0101 ?
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Binary Drill Solutions
1101 13
1001 9
1010 10
1000 8
0101 5
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Hexadecimal (Base 16)
163 162 161 160
So 3816 what in decimal?
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Hexadecimal Solution
3816 5610
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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
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Hexadecimal Drill
2B7 what in decimal?
Hint Think 163 162 161 160
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Hexadecimal Drill Solution
Hint Think 163 162 161 160
2B7 256 x 2 16 x 11 7
2B716 69510
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Hexadecimal To Binary
2B7 what in binary?
Hint Secret Recipe Convert digit by digit!!!
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Hex2Bin Solution
2B7 what in binary?
Secret Recipe Convert digit by digit!!!
2 B 716 0010 1011 0111
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Octal (Base 8)
83 82 81 80
So 658 what in decimal?
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Octal Solution
658 5310
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Decimal - Octal
0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8
10 9 11 10 12
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Octal Drill
2178 what in decimal?
Hint Think 83 82 81 80
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Octal Drill Solution
Hint Think 83 82 81 80
2178 64 x 2 8 x 1 7
2178 14310
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Octal To Binary
2178 what in binary?
Hint Groups of 3 Secret Recipe Convert digit
by digit!!!
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Oct2Bin Solution
217 what in binary?
Secret Recipe Convert digit by digit!!!
2 1 78 010 001 111
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Fractions in Binary
23 22 21 20 . 2-1
2-2 2-3
21.75 what in binary?
2 1.7510 10101. 11
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Fractions Drill
23 22 21 20 . 2-1
2-2 2-3
41.6875 what in binary?
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Fractions Drill
23 22 21 20 . 2-1
2-2 2-3
41.687510 101001.1011
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Complements
1s complement is formed by inverting the digits
1s complement of 10010001 01101110
2s complement is formed by adding 1 to the 1s
complement
2s complement of 10010001 01101111
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Negative (signed) Numbers
2s 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
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BCD (Binary Coded Decimal)
Example 87510 1000 0111 0101 Note that each
digit is coded individually. Do not confuse this
with pure binary!
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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
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Error Detection and Parity
Parity bit is an extra bit added to make the
total number of 1s 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.
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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.
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Logic Gates
AND OR x y x ? y x y xy
0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1
1
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Digital Logic Gates
AND OR NOT
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Timing Diagrams
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Thats All Folks!