Exam 1 & 2 Questions

Question 1

Define combinational circuit in a few sentences and give two examples.

Answer 1

A combinational circuit is a type of logic circuit where the output depends only on the current inputs and not on past inputs. Examples include adders and multiplexers.

Question 2

Define implicant and give two examples assuming a circuit with three inputs: A, B, C.

Answer 2

An implicant is a group of minterms that can be combined to simplify a Boolean function. Examples:
AB and A’C

Question 3

Define maxterm and provide one example assuming a circuit with five inputs: A, B, C, D, E.

Answer 3

A maxterm is a sum term that gives 0 for exactly one input combination. Example:
A+B’+C+D+E’

Question 4

Define Implicant, Prime Implicant, and Essential Prime Implicant and give one example of
each assuming the circuit has three inputs equal to: A, B, C.

Answer 4

Implicant: A group of minterms that can be combined (e.g., AB)

Prime Implicant: An implicant that can’t be combined further (e.g., AB in a K-map).

Essential Prime Implicant: A prime implicant covering a minterm that no other implicant covers (e.g., A’C if it is the only one covering a certain minterm).

Question 5

What is the difference between a combinational circuit and a sequential circuit?

Answer 5

A combinational circuit has outputs that depend only on the current inputs, while a sequential circuit has outputs that depend on both current inputs and past states (memory).

Question 6

Convert
45 base 10
​ to binary.

Answer 6

101101 base 2

Question 7

What are the three methods for representing negative binary numbers?

Answer 7

Sign & magnitude, 1’s complement, and 2’s complement.

Question 8

What is the function of a multiplexer in digital circuits?

Answer 8

A multiplexer (MUX) selects one input from multiple inputs and forwards it to the output based on select lines.

Question 9

What is a decoder, and where is it used?

Answer 9

A decoder converts binary input into a unique output line. It is used in memory addressing and data demultiplexing.

Question 10

What is the Boolean expression for a half-adder?
A:

Answer 10

Sum = A⊕B
Carry = AB

Question 11

What is the difference between synchronous and asynchronous sequential circuits?

Answer 11

Synchronous circuits update their state at clock pulses, while asynchronous circuits change states as soon as the input changes, without a clock.