boolean operations
DESCRIPTION
Boolean Operations. 1 and 1 = 1. Boolean Algebra. Boolean Logic Logical rules for dealing with true/false values Examples: You get an F if you skip the test OR if you get below 60 You can register for CS161 if you have taken CS160 AND you have taken MTH111. Boolean Operators. - PowerPoint PPT PresentationTRANSCRIPT
Boolean Operations1 and 1 = 1
Boolean Algebra
• Boolean Logic– Logical rules for dealing with
true/false values
• Examples:– You get an F if you skip the test OR if you get below 60– You can register for CS161 if you have taken
CS160 AND you have taken MTH111
Boolean Operators
• Boolean Operations– Combine/modify boolean values– Computers implements as logic gate circuits
Or Rule
• OR rule– 1 if either input is 1– 0 if they both are 0
Or Rule
• Logic rules implemented as circuits• Can represent anything with true/false values
You get an F if you skip the test OR if you get below 60
And Rule
• AND produces – 1 if both inputs are 1– 0 if either is 0
And Rule
• On/Off can stand for any true/false idea– You can register for CS161 if you have taken
CS160 AND you have taken MTH111
Boolean Operators
• Truth Table :– Shows every combination of inputs and their
output
Input1 Input2 Out
0 0 0
0 1 1
1 0 1
1 1 1
Basic Rules – 1 input
• NOT– Output is 1 if input is 0– Output is 0 if input is 1
If it is not raining my drive is easier
In Out
0 1
1 0
Basic Rules – 2 inputs
• AND– 1 if both inputs 1– 0 otherwise
• OR– 1 if either input is 1 – 0 if both are 0
• XOR (exclusive OR)– 1 if only one input is 1– 0 if both inputs are 0 or 1
In1 In2 Out
0 0 0
0 1 0
1 0 0
1 1 1In1 In2 Out
0 0 0
0 1 1
1 0 1
1 1 1
In1 In2 Out
0 0 0
0 1 1
1 0 1
1 1 0
OR vs XOR
• In English "or" used for OR and XOR
– You can either pick up your room or you can come help do the laundry
– You can have an ice cream cone or a two cookies
Not Rules
• OR– 1 if either input is 1 – 0 if both are 0
• NOR (not OR)– 0 if either input is 1 – 1 if both are 0
In1 In2 Out
0 0 0
0 1 1
1 0 1
1 1 1
In1 In2 Out
0 0 1
0 1 0
1 0 0
1 1 0
• "Not" rules do opposite:
Other NOT rules
• AND
• XOR
In1 In2 Out
0 0 0
0 1 0
1 0 0
1 1 1
In1 In2 Out
0 0 0
0 1 1
1 0 1
1 1 0
• NAND
• XNOR
In1 In2 Out
0 0 1
0 1 1
1 0 1
1 1 0
In1 In2 Out
0 0 1
0 1 0
1 0 0
1 1 1
Applying rules
• Rules only work on two inputs• Bit sequences processed on bit at a time
EX: Combine with ORInput0: 0 0 1 0
Input1: 1 0 1 0
Output:
Combining Bits
• Can apply a rule to combine two bit sequences:– Apply rule to each pair
EX: Combine with OR
Input0: 0 0 1 0
Input1: 1 0 1 0
Output: 0
Combining Bits
• Can apply a rule to combine two bit sequences:– Apply rule to each pair
EX: Combine with OR
Input0: 0 0 1 0
Input1: 1 0 1 0
Output: 1 0
Combining Bits
• Can apply a rule to combine two bit sequences:– Apply rule to each pair
EX: Combine with OR
Input0: 0 0 1 0
Input1: 1 0 1 0
Output: 0 1 0
Combining Bits
• Can apply a rule to combine two bit sequences:– Apply rule to each pair
EX: Combine with OR
Input0: 0 0 1 0
Input1: 1 0 1 0
Output: 1 0 1 0