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## Digital Electronics

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**Chapter 1**Binary Systems**Digital Electronics Galore!**• Digital Cameras • Digital Versatile Disks (DVD) • Digital Computers • Digital Televisions • Digital Telephones • Digital Birthday Cards**Binary Numbers**7 5 8 3 Decimal 103 102 101 100 Binary 1 1 0 1 23 22 21 20**Binary Drill**1101 = ? 1001 = ? 1010 = ? 1000 = ? 0101 = ?**Binary Drill … Solutions**1101 = 13 1001 = 9 1010 = 10 1000 = 8 0101 = 5**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**Hint: Think … 163 162 161 160 2B7 = 256 x 2 + 16 x 11 + 7 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**Hint: Think … 83 82 81 80 2178 = 64 x 2 + 8 x 1 + 7 2178 = 14310**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**23 22 21 20 . 2-1 2-2 2-3 21.75 = what in binary? 2 1.7510 = 10101. 11**Fractions … Drill**23 22 21 20 . 2-1 2-2 2-3 41.6875 = what in binary?**Fractions … Drill**23 22 21 20 . 2-1 2-2 2-3 41.687510 = 101001.1011**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