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WorksheetsMATH ELECTIVES (Digital Design and Symbolic Computation)
Total questions: 61
Worksheet time: 1hrs 3mins
Which of the following is NOT a fundamental logic gate?
AND
OR
NOT
MAGI
What is the primary purpose of Boolean algebra?
To perform arithmetic operations on integers.
To represent and manipulate logical expressions.
To analyze the behavior of analog circuits.
To model the stock market.
Karnaugh maps are primarily used for:
Designing complex microprocessors.
Analyzing analog signals.
Simplifying Boolean expressions.
Predicting stock market trends.
Which of the following is NOT a type of flip-flop?
JK
SR
DT
MX
Finite State Machines (FSMs) are used to model systems with:
Continuous inputs and outputs.
Discrete states and transitions.
Random behavior.
No memory
The XOR gate produces a HIGH output only when both inputs are HIGH.
TRUE
FALSE
Decoders convert binary code to a set of unique output signals.
TRUE
FALSE
A multiplexer selects one of multiple inputs based on a control signal.
TRUE
FALSE
Registers are collections of interconnected flip-flops.
TRUE
FALSE
Sequential logic circuits have no memory.
TRUE
FALSE
Identify the logic gate whose output is HIGH only when all inputs are HIGH.
(a)
Identify the Boolean theorem that states A + AB = A.
(a)
Two key characteristics of sequential logic circuits:
Identify the type of flip-flop known for its ability to toggle its output.
(a)
Identify a common application of shift registers.
(a)
Identify the type of logic circuit where the output depends only on the current input combinations.
(a)
three common simplification techniques used in Boolean algebra.
Four types of combinational logic circuits:
Three types of flip-flops:
Two applications of finite state machines:
Solve the problems where, A = 2, B = 3, C = 4.
Commutative Laws
A *B = B *A
Solve the problems where, A = 2, B = 3, C = 4.
Commutative Laws
A + B = B + A
Solve the problems where, A = 2, B = 3, C = 4.
Associative Laws
(A + B) + C = A + (B + C)
Solve the problems where, A = 2, B = 3, C = 4.
Associative Laws
(A *B) C = A * (B *C)
Solve the problems where, A = 2, B = 3, C = 4.
Distributive Laws
A* (B + C) = A * B + A * C
Solve the problems where, A = 2, B = 3, C = 4.
Distributive Laws
A + (B *C) = (A + B) (A + C)
Provide the output for Logical Operator #1
(a)
Provide the output for Logical Operator #2
(a)
Provide the output for Logical Operator #3
(a)
Provide the output for Logical Operator #4
(a)
Provide the output for Logical Operator #5
(a)
Provide the output for Logical Operator #6
(a)
Provide the output for Logical Operator #7
(a)
Provide the output for Logical Operator #8
(a)
Provide the output for Logical Operator #9
(a)
Provide the output for Logical Operator #10
(a)
Provide the output for Logical Operator #11
(a)
Provide the output for Logical Operator #12
(a)
Provide the output for Logical Operator #13
(a)
Provide the output for Logical Operator #14
(a)
Provide the output for Logical Operator #15
(a)
Provide the output for Logical Operator #16
(a)
Which of the following operations is performed using XOR in GF(2) matrix operations?
Multiplication
Addition
Inverse
Determinant
A matrix used to represent a linear transformation is called a:
State diagram
Truth table
Transformation matrix
Boolean expression
The set of vectors that are mapped to the zero vector by a linear transformation is known as the:
Image
Rank
Kernel
Nullity
Linear Feedback Shift Registers (LFSRs) primarily utilize which mathematical structure?
Boolean Algebra
Graph Theory
Calculus
Linear Algebra
Which of the following is used to detect and correct errors in digital communication?
Error-correcting codes
Digital Signal Processing
Combinational Logic
Finite State Machines
1. Matrix multiplication in GF(2) is identical to standard integer matrix multiplication.
True
False
The kernel of a linear transformation is always the set of all possible output vectors
True
False
Eigenvalues are always zero in GF(2) matrices.
True
False
The rank of a matrix plus its nullity equals the dimension of the domain.
True
False
GF(2) is a finite field with only two elements, 0 and 1.
True
False
In GF(2), the operation equivalent to the AND logic gate is (a) .
The dimension of the kernel of a linear transformation is called the (a) .
(a) are used to process digital signals like audio and images.
A matrix that, when multiplied by the original matrix, results in the identity matrix is called the (a) .
The set of all possible output vectors of a linear transformation is called the (a) .
The set of all possible output vectors of a linear transformation is called the (a) .
Matrix Addition (GF(2)):
[[1, 0], [1, 1]] + [[0, 1], [1, 0]] = (a)
Matrix Multiplication (GF(2)):
[[1, 0], [1, 1]] * [[0, 1], [1, 0]] = (a)
Scaling:
If s = 3, the vector (2, 3) would be transformed to (a)
