Binary Operations

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When working with binary numbers, there are three logical operations not found in normal math:

• AND
• OR
• and XOR

AND

To perform the AND operation:

• you take two binary numbers and compare them one place at a time

• If both numbers have a 1 in both places, then the resultant number is a 1

• If not, then the resultant number is a 0

• e.g.,

  

OR

• OR operation checks to see whether there is a 1 in either or both numbers in a given place

• If so, then the resultant number is 1

• If not, the resultant number is 0

• e.g.,

  

XOR

The exclusive OR (XOR ) checks to see whether there is a 1 in a number in a given place, but not in both numbers at that place.

• If it is in one number but not the other

  • then the resultant number is 1

• If not, the resultant number is 0

• e.g.,

  

• XOR is reversible

  • XOR the resultant number with the second number and you get the first number