Digital Electronics Chapter 1 Binary Systems Digital Electronics Galore! Digital Cameras Digital Versatile Disks (DVD) Digital Computers Digital Televisions.

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Presentation transcript:

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 Decimal Binary

Binary Drill 1101 = ? 1001 = ? 1000 = ? 0101 = ? 1010 = ?

Binary Drill … Solutions 1101 = = = = = 10

Hexadecimal (Base 16) So = what in decimal?

Hexadecimal Solution = 56 10

Decimal - Hexadecimal 0 through 9 = 0 through 9 10 = A 11 = B 12 = C 13 = D 14 = E 15 = F 16 = = = 12

Hexadecimal Drill 2B7 = what in decimal? Hint: Think …

Hexadecimal Drill … Solution 2B7 = 256 x x Hint: Think … B7 16 =

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 7 16 =

Octal (Base 8) So 65 8 = what in decimal?

Octal Solution 65 8 = 53 10

Decimal - Octal 0 = 0 1 = 1 2 = 2 3 = 3 4 = 4 5 = 5 6 = 6 7 = 7 8 = 10 9 = = 12

Octal Drill = what in decimal? Hint: Think …

Octal Drill … Solution = 64 x x = Hint: Think …

Octal To Binary = 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!!! =

Fractions in Binary = what in binary? =

Fractions … Drill = what in binary?

Fractions … Drill =

Complements 1’s complement is formed by inverting the digits 1’s complement of = ’s complement is formed by adding 1 to the 1’s complement 2’s complement of =

Negative (signed) Numbers 2’s complement is used to represent a negative number Example: = and 102 = So -102 = So 115 = = =

BCD (Binary Coded Decimal) Example = Note that each digit is coded individually. Do not confuse this with pure binary!

ASCII Character Codes CAPS:A = = G = = Z = 5A 16 = lower casea = = h = = z = 7A 16 = digits = = = =

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 = A with odd parity = 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 ANDOR xy x  y xy x+y

Digital Logic Gates AND OR NOT

Timing Diagrams

That’s All Folks!