Assignment 2: Boolean Logic
Due Date: Feb. 11, 2016
1. Draw the logic diagrams with gates for the following Boolean functions (30 pts)
1) 𝑌 = 𝐴 + 𝐵 ∙ 𝐶
̅̅̅̅̅̅̅̅
2) 𝑌 = (𝐴̅ + 𝐵̅ ) ∙ 𝐶 + 𝐴 ∙ (𝐵
+ 𝐶)
̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
3) 𝑌 = ̅̅̅̅̅̅̅̅
𝐴̅ + 𝐵̅ + 𝐶 ∙ (𝐴 + 𝐷)
2. (15 pts) Prove or disprove
𝐴 + 𝐴̅ ∙ 𝐵̅ = 𝐴 + 𝐵̅ .
(Hint: Use a truth table)
3. (15 pts) Use De Morgan’s law and the other Boolean logic laws to prove that
(𝐵 ∙ 𝐶 )
((𝐴 ∙ 𝐵) + (𝐴 ∙ 𝐶)) ∙ ̅̅̅̅̅̅̅̅̅̅
is equivalent to:
(𝐴 ∙ 𝐵 ∙ 𝐶̅ ) + (𝐴 ∙ 𝐶 ∙ 𝐵̅ ).
4. (20 pts) Show that using only two-input NOR gates can build the AND, OR, NOT, and XOR
functions.
5. (20 pts) Assume that X consists of 4 bits, X3, X2, X1, X0. Write three logic functions that are
true if and only if
a. X contains only one 1
b. X contains an even number of 1’s
c. X when interpreted as an unsigned binary number is less than 10