Switching Circuits & Logic Design, Fall 2023
Quiz #1
09/22, 3:30pm-4:20pm
(Cannot Use Karnaugh-Map for Logic
Minimization/Simplification!)
Problem 1: (8+8+4 points)
(a) Given the summation (2222)𝑅 + (4321)𝑅 = (12043)𝑅 under some radix R,
determine the minimum possible value of 𝑅 and the corresponding decimal value
of (12043)𝑅 .
(b) Construct a table for 7-3-2-1 weighted code.
(c) Write the decimal value of (12043)𝑅 in part (a) using 7-3-2-1 weighted code
derived in part (b).
Problem 2: (10+12 points)
The following switching circuit is used to implement the logic function of 𝐹(𝐴, 𝐵, 𝐶).
𝐹 = 1 if node a is connected to node b; otherwise 𝐹 = 0:
(a) Draw the corresponding circuit of logic gates using only NOT, AND, and OR
gates.
(b) Derive an equivalent switching circuit using 2 switches.
aa
b
Problem 3: (12+10 points)
In the following circuit, 𝐹 = (𝐴′ + 𝐵)𝐶.
(a) Write down the truth table for 𝐺 so that 𝐻 is as specified in its truth table.
(b) What is the 5-term sum-of-product form of 𝐺? (i.e., 5 product terms in SOP.)
Problem 4: (6+6+6+6 points)
Are the following statements or identities always true? If yes, please give a brief
explanation; otherwise, give a counter example.
(a) If 𝐴 + 𝐵 = 𝐶, then 𝐴𝐷′ + 𝐵𝐷′ = 𝐶𝐷′
(b) If 𝐴𝐷′ + 𝐵𝐷′ = 𝐶𝐷′ , then 𝐴 + 𝐵 = 𝐶
(c) If 𝐴⨁𝐵⨁𝐶⨁𝐷 = 1, then 𝐴𝐵𝐶 + 𝐴𝐵𝐷 + 𝐴𝐶𝐷 + 𝐵𝐶𝐷 = 1
(d) If 𝑋⨁𝑌 = 𝑍, then 𝑍⨁𝑋 = 𝑌
Problem 5: (12 points)
Write the Boolean expression of 𝐹(𝐴, 𝐵, 𝐷), and simplify algebraically (i.e., no Kmap tricks for logic simplification) to obtain a sum of 3 product terms for 𝐹: