06 - Distribution

 1. The distributive/distribution law can also be stated like this: a × (b + c) = a × b + b × a



 2. The Boolean distributivity law is similar to distributivity in normal mathematics and has to do with expanding or simplifying ___________

  full stops

  AND gates


  NOT gates

 3. In practice, distribution is often carried out when either an 'AND' or an 'OR' is outside the brackets and the other is inside.



 4. You can think of the distributive law as a law which deals with either 'multiplying out' or factoring. E.g in Maths: x(y+z) could give you:





 5. Complete the following equation: e AND (f OR g) = (e AND f) OR (e AND g) and e OR (f AND g) = (e OR f) AND _________



  (e OR g)

  (e AND g)

 6. The distributive law would allow us to arrive at what output, from this expression: (x+y).(x+z)=





 7. Using the distributive law, "simplify" the following expression: (A + B)(A + C)

  A.1 + B.C

  A.1 + B.C + C


  A.A + A.C + A.B + B.C

 8. Using the distributive law it is also possible to simplify (A + B).(A + C) to A(1 + B) + B.C



 9. The expression (A + B)(A + C) can be simplified to ____________using the distributive law.


  A + (B.C)



 10. Using the distributive law: X + Y Z = (X + Y) + (X. Z)



 11. Using the distributive law: X. (Y + Z) = X Y + Z



 12. Using the distributive law: X. (Y + Z) = X Y + X Z



 13. Read the excerpt on removing factors below and fill in the blanks for the boolean equivalent
Using the distributive law, you can also remove factors 
(common variables), like in normal algebra. 

For example: if you had (3 * 4) + (3 * 2), this could be 
factorised into 3(4 + 2). 

Note that both answers give 18. 

The Boolean equivalent of this is:


  (A AND B) OR (A AND C) ? A OR B OR C

  (A AND B) OR (A AND C) ? A AND (B OR C)

  (A AND B) OR (A AND C) ? ABC

  (A AND B) OR (A AND C) ? A AND B

 14. A(B + C) =

  A.B + A.C

  A.B. A.C

  A+.B + A+C


 15. A + (B.C) =

  (A + B).(A + C)

  (A. B).(A.C)

  (A. B)+(A.C)