Digital Electronics Chapter 1 Binary Systems Digital Electronics

Digital Electronics

Chapter 1 Binary Systems

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Binary Numbers Decimal 7 5 8 3 102 101 100 Binary 1 1 0 1 23 22 21 20

Binary Drill 1101 = ? 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 2 B 7 = what in decimal? Hint: Think … 163 162 161 160

Hexadecimal Drill … Solution Hint: Think … 163 162 161 160 2 B 7 = 256 x 2 + 16 x 11 + 7 2 B 716 = 69510

Hexadecimal To Binary 2 B 7 = what in binary? Hint Secret Recipe: Convert digit by digit!!!

Hex 2 Bin … Solution 2 B 7 = 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!!!

Oct 2 Bin … 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 = 0110 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 = 5 A 16 = 1011010 lower case a = 6116 = 1100001 h = 6816 = 0111000 z = 7 A 16 = 1111010 digits 0 -9 4 = 3416 = 0110100 8 = 3816 = 0111000

Error Detection and 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 0 0 0 0 1 1 1 0 0 1 1 1 1

Digital Logic Gates AND OR NOT

Timing Diagrams

That’s All Folks!