Number Systems and Conversions Quiz

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Convert the decimal number 26110 to hexadecimal. What is the correct hexadecimal representation?

1B5h

105h (correct)

FFh

16h

What is the binary equivalent of the hexadecimal value A3C5H?

1100 1000 1101 1101B

1010 0011 1100 0101B (correct)

1010 0111 1100 0101B

1010 0011 0100 0101B

Which of the following represents the octal number 247 in hexadecimal?

A7H (correct)

016H

A6H

009H

What is the octal representation of the decimal number 48710?

7478 Signup and view all the answers

Convert the binary number 10001011001011B to hexadecimal. What is the resulting hexadecimal value?

2CBH Signup and view all the answers

What is the fractional hexadecimal equivalent for the decimal number 36.5328?

1E.AD16 Signup and view all the answers

If the binary number 10110B is converted to decimal, what is the resulting decimal value?

22 Signup and view all the answers

What is the 10's complement of the decimal number 23450?

76550 Signup and view all the answers

In converting the fractional part 0.6875 to binary, what binary representation is obtained?

.1011 Signup and view all the answers

Using 9's complement subtraction, what would be the result of subtracting 1000 from 1234?

234 Signup and view all the answers

What is the 2's complement of the binary number 1011001?

0100111 Signup and view all the answers

Which of the following represents the 16's complement of the hex number 4A30?

B5D0 Signup and view all the answers

What is the correct method to find 9's complement for the number 23450?

99999 - 23450 Signup and view all the answers

When performing 10's complement subtraction of 3000 from 1234, what is the correct answer?

-1766 Signup and view all the answers

What will be the 4's complement of the decimal number 224?

220 Signup and view all the answers

What is the result of applying De Morgan's theorem to the expression (A + B + C)'?

A' + B' + C' Signup and view all the answers

In simplifying the expression a.b `+ a.(b + c)` + b.(b + c)`, which property is utilized when reducing b.b` to 0?

Complementarity Signup and view all the answers

Which form is NOT a canonical form as mentioned in the content?

Mixed Product and Sum (MPS) Signup and view all the answers

What is the simplified form of the expression A'B'C + A'BC + AB'?

A'C + AB' Signup and view all the answers

When simplifying the function F = AB + (AC)' + AB'C(AB + C), which step eliminates AB or C permanently as contributing factors?

Applying Absorption Signup and view all the answers

What does the additive inverse define in arithmetic operations?

Subtraction Signup and view all the answers

Which of the following correctly represents the multiplication identity property?

A * 1 = A Signup and view all the answers

According to the distributive law, which expression is equivalent to A * (B + C)?

A * B + A * C Signup and view all the answers

What does Theorem 4(Associative) indicate about addition?

A + (B + C) = (A + B) + C Signup and view all the answers

In De Morgan’s Theorems, what does (A.B)′ equal?

A' + B' Signup and view all the answers

What is the result of applying Theorem 2(b): A * 0?

0 Signup and view all the answers

Which of the following statements is accurate regarding the properties discussed?

A + A = A Signup and view all the answers

What is the complementary result of A + A' based on Postulate 5?

1 Signup and view all the answers

Based on Theorem 6(b), what does A.(A + B) equal?

A Signup and view all the answers

What does the Involution theorem state about negation and double negation?

(A')' = A Signup and view all the answers

What is the primary function of a diode array in electronic circuits?

To dissipate and divert surge voltages Signup and view all the answers

Which type of IC classification would include devices with 10,000 to 99,999 circuits?

VLSI Signup and view all the answers

What is a disadvantage of integrated circuits (ICs) mentioned in the context?

Coils or inductors cannot be fabricated within them Signup and view all the answers

Which of the following best describes monolithic ICs?

ICs fabricated within a single continuous piece of silicon Signup and view all the answers

Which attribute is NOT associated with diode arrays?

Very high clamping voltage Signup and view all the answers

In the context of scale of integration, which category handles 100 to 9,999 circuits?

LSI Signup and view all the answers

Which of these is a merit of ICs?

Reduced cost of production Signup and view all the answers

Which type of IC is formed by inter-connecting individual chips?

Hybrid ICs Signup and view all the answers

What maximum number of components can ULSI ICs handle?

10,000,000 Signup and view all the answers

Which statement about digital logic ICs does NOT hold true?

They are immune to electrostatic discharge. Signup and view all the answers

Study Notes

Course Information

Course Title: Digital Logic Design
Course Code: IFT 211

Number Systems

Computers use the binary (base 2) number system
Binary numbers are represented using 0s and 1s
Other number systems include octal (base 8) and hexadecimal (base 16)
These are used as a shorthand or compact form for representing binary numbers

Binary (Base 2) Number System

Examples of converting binary to decimal
10110₂ = 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 22₁₀

Decimal (Base 10) Number System

Example of converting decimal to decimal
735₁₀ = 7×10² + 3×10¹ + 5×10⁰ = 700 + 30 + 5 = 735₁₀

Hexadecimal (Base 16) Number System

Example of converting hexadecimal to decimal
A3EH₁₆ = 10×16² + 3×16¹ + 14×16⁰ = 2560 + 48 + 14 = 2622₁₀

Binary-Decimal-Hexadecimal Conversion Table

A table converting hexadecimal, binary and decimal equivalent values.

Decimal to Binary Conversion

Example: Converting decimal 211 to binary
2¹⁰⁵₁₀ = 11010011₂

Decimal to Hexadecimal Conversion

Example: Converting decimal 261 to hexadecimal.
261₁₀ = 105₁₆

Binary to Decimal Conversion

Example: Converting binary 10110₂ to decimal. 10110₂ = 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 22₁₀

Decimal to Octal Conversion

Example: Converting decimal 487 to octal
487₁₀ = 747₈

Binary to Hexadecimal Conversion

Example: Converting binary 1001001010₂ to hexadecimal
1001001010₂ = 24AH₁₆

Hexadecimal to Binary Conversion

Example: Converting hexadecimal A3C5H to binary
A3C5₁₆ = 1010 0011 1100 0101₂

Hexadecimal to Octal Conversion

Example: Converting hexadecimal A72E₁₆ to octal.
A72E₁₆ = 123456₈

Octal to Hexadecimal Conversion

Example: Converting octal 247₈ to hexadecimal.
247₈ = A7₁₆

10's Complement

Example: Finding the 10's complement of 23.234
23.234 ten's complement = 76.676

9's Complement

Example: Finding the 9's complement of 23450₁₀
9's complement of 23450₁₀ = 76549₁₀

8's Complement

Example: Finding the 8's complement of 2450₈
8's complement of 2450₈ = 5330₈

16's Complement

Example: Finding the 16's complement of 4A30₁₆
16's complement of 4A30₁₆ = B5D0₁₆

R's and R-1 Compliments

Formulas for R's complement and (R-1) complement.
Example showing converting 1011001₁₀ to 2's complement, based on above formula

2's complement of Hexadecimal

Technique to find 2's complement for a given value in hexadecimal

Complements

Example showing 4's complement, 5's complement, 9's complement, and 10's complement calculation

9's Complement Subtraction

Example: Subtracting 1000 from 1234 using 9's complement method
1234 + 8999 = 10233 - 1 = 234

10's Complement Subtraction

Example of subtracting 1000 from 1234 using 10's complement method

Circuit diagrams

Examples of circuit diagrams for various digital circuits

Binary Codes

Binary code representation and weighted binary codes, e.g., BCD
Excess-3 code examples

BCD Code

Example of decimal to BCD conversion
85₁₀= 1000 0101 (BCD)
572₁₀= 0101 0111 0010 (BCD)
8579₁₀ = 1000 0101 0111 1001 (BCD)

BCD to Decimal Conversion

Example: Converting 1001₂ to decimal. 1001₂ = 9₁₀

Excess-3 Code

Calculation example to convert 15 to an excess-3 code, where 3 is added to each digit.
Example conversion of 237.75₁₀ to excess-3 code
Example: Calculation, given an excess-3 code, find decimal equivalent, based on above calculation

Gray Code

Gray code representation in a table
Conversion examples of converting binary to gray code, based on diagram.
Conversion examples of converting gray code to binary, based on diagram

BCD Addition

Example shows how 476 and 394 are to be add using BCD

Excess-3 Addition

Example shows how 45 and 38 are to be added using Excess-3 code

Don't-care Combination

Concept of don't-care conditions in digital systems
Example showing how don't-care conditions are shown in a K-map to simplify a given function

K-maps

Explanation of Karnaugh maps for simplifying Boolean expression
Example of K-maps simplifying various Boolean expressiion

Sequential Circuits

Diagram showing the blocks of a sequential circuit.
Explanation of bistable and synchronous/asynchronous system

Latches

Diagrams showing SR latch designs using NOR gates.

Flip-Flops

Diagrams showing flip-flop designs using NAND gates, SR, JK, D and T flip-flops (constructions and truth table)

Designing Combinatorial Circuits

Steps in designing combinatorial circuitry (i.e. obtaining a Boolean expression)
Example and implementation, based on the calculation steps.

Half Adder

Example of half adder truth table, its equation, and implementation of sum using XOR logic.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of various number systems including decimal, hexadecimal, binary, and octal. This quiz explores conversions between these systems and covers topics like 9's and 2's complements. Perfect for students in math or computer science courses.