Paper 2 Boolean Algebra Flashcards
(11 cards)
4.6.5.1 Using Boolean Algebra: What is Boolean algebra?
A branch of algebra dealing with variables whose values are TRUE (1) or FALSE (0). It is used to simplify digital logic circuits and logical expressions.
4.6.5.1 Using Boolean Algebra: What are the main Boolean operators and their symbols?
The main operators are AND (conjunction, . or ∧), OR (disjunction, + or ∨), and NOT (negation, an overbar or ¬).
4.6.5.1 Using Boolean Algebra: What is the Identity Law?
The Identity Law states that a variable remains unchanged when combined with an identity element. The identities are A + 0 = A and A . 1 = A.
4.6.5.1 Using Boolean Algebra: What is the Complement Law?
The Complement Law (or Inverse Law) involves a variable and its opposite, which always results in a constant. The laws are A + ¬A = 1 and A . ¬A = 0.
4.6.5.1 Using Boolean Algebra: What is the Distributive Law?
The Distributive Law allows for multiplying or factoring out expressions. The laws are A.(B + C) = A.B + A.C and the less obvious A + (B.C) = (A + B).(A + C).
4.6.5.1 Using Boolean Algebra: What is De Morgan’s Law?
De Morgan’s Law describes how to negate a group of variables. The laws are ¬(A + B) = ¬A . ¬B and ¬(A . B) = ¬A + ¬B, often remembered as “break the bar, change the sign.”
4.6.5.1 Using Boolean Algebra: What is the Absorption Law?
The Absorption Law simplifies expressions where a variable is combined with a term containing that same variable. The laws are A + (A . B) = A and A . (A + B) = A.
4.6.5.1 Using Boolean Algebra (Easy): Simplify the expression F = A + (¬A . B)
F = A + B. First, apply the Distributive law: (A + ¬A).(A + B). Then apply the Complement law (A + ¬A = 1) to get 1.(A + B), and finally the Identity law gives A + B.
4.6.5.1 Using Boolean Algebra (Medium): Simplify the expression F = ¬(¬A + B) + B
F = A + B. First, apply De Morgan’s Law to get (¬(¬A) . ¬B) + B. Then use Double Negation to get (A . ¬B) + B. Finally, use Distribution to get (B + A).(B + ¬B), which simplifies to A + B using Complement and Identity laws.
4.6.5.1 Using Boolean Algebra (Hard): Simplify the expression F = A.B + A.(B + C) + B.(B + C)
F = B + A.C. First, expand all terms using the Distributive law: A.B + A.B + A.C + B.B + B.C. Using the Idempotent law (X.X=X, X+X=X), this becomes A.B + A.C + B + B.C. Using the Absorption law (B + B.C = B), we get A.B + A.C + B. Finally, applying Absorption again (B + A.B = B) gives the final answer: B + A.C.
