1. 1 4. Computer Maths and Logic 4.2 Boolean Logic

2. 4.2.1 Boolean Operators

3. 3 Boolean logic This is concerned only with the values true (1) and false (0). In the statement “if it is warm and not raining then we will go for a picnic” you can substitute all 3 parts with true or false, depending on the conditions.

4. 4 Boolean operators True/false statements can be worked on using the following boolean operators: ‣ AND ‣ OR ‣ NOT ‣ XOR

5. 5 Boolean operators Usually, you are combining 2 or more statements (the inputs) into one result (the output). Note the similarity with normal algebra, e.g. ‣ 3 x 4 = 12 ‣ where the x operator combines two inputs into one output.

6. 6 AND Both inputs must be true for the output to be true. Symbol: e.g. A B = C So, 'if it is warm and sunny then we will go for a picnic' becomes ‣ 'If (it is warm it is sunny) = go for a picnic' ‣ A B = C where A = sunny, B = warm, C = picnic Note that it has got to be both.

7. 7 AND in Java Use two ampersands (&&): ‣ boolean sunny, warm, goToBeach; if (sunny && warm) { goToBeach = true; } else { goToBeach = false; }

8. 8 OR Only one input need be true for the output to be true. Symbol: + e.g. A + B = C So, ‘if it is warm or it is sunny then we’ll go for a picnic' becomes ‣ if (it is warm + it is sunny) = go for a picnic' ‣ A + B = C where A = sunny, B = warm, C = picnic This means we are not so fussy (warm and cloudy OK, cool and sunny OK, but not cool and cloudy).

9. 9 OR in Java Use two break bars (||): ‣ boolean sunny, warm, goToBeach; if (sunny || warm) { goToBeach = true; } else { goToBeach = false; }

10. 10 NOT This simply reverses the truth of the input. Symbol: o ̅̅ v ̅ e ̅ r ̅ l ̅ i ̅ n ̅ e ̅ e.g. A B ̅ = C So, ‘if it’s warm and it’s not raining then we’ll go for a picnic' becomes ‣ if (it’s warm it ̅ ’ ̅ s ̅ ̅ r ̅ a ̅ i ̅ n ̅ i ̅ n ̅ g ̅ ) = go for a picnic' ‣ A B ̅ = C where A = warm, B = rain, C = picnic This means it must be warm and it must NOT be raining.

11. 11 NOT in Java Use the exclamation mark (!) boolean sunny, warm; if (!warm) { if (temp != 0) { output(“Good for mountain biking."); } }

12. 12 XOR The exclusive OR - one or the other but not both. Symbol: ⊕ e.g A ⊕ B = C. So, ‘if it’s warm or sunny but not both, we’ll go for a picnic’ becomes ‣ ‘if (it’s warm ⊕ it’s sunny) = we’ll go for a picnic’ ‣ A ⊕ B = C where A = warm, B = sunny, C = picnic This means warm and cloudy OK, cool and sunny OK, but not cool and cloudy and not warm and sunny.

13. 13 NAND and NOR The equivalent of doing AND / OR then reversing the result. Symbols: ̅ e.g. A ̅ B = C and + ̅ e.g. A + ̅ B = C. ‣ ‘If it is not (warm and sunny) then we are going for a picnic.’ ‣ ‘If it is not (warm or sunny) then we are going for a picnic.’ Can these be said another way?