Podcast
Questions and Answers
What is the value of the binary number (1101)2 in decimal?
What is the value of the binary number (1101)2 in decimal?
- 15
- 13 (correct)
- 12
- 14
Which of the following is true about the octal number system?
Which of the following is true about the octal number system?
- It represents the decimal number (8)10 as (10)8. (correct)
- It uses digits 0 to 8.
- It has a base of 10.
- It includes digits from 0 to 9.
How many digits are used in the binary number system?
How many digits are used in the binary number system?
- Three digits: 0, 1, and 2.
- Four digits: 0, 1, 2, and 3.
- Eight digits: 0 to 7.
- Two digits: 0 and 1. (correct)
What is the base of the hexadecimal number system?
What is the base of the hexadecimal number system?
Which of the following correctly demonstrates the decimal conversion formula and its application for the number (332)10?
Which of the following correctly demonstrates the decimal conversion formula and its application for the number (332)10?
What is the result of removing the radix point before finding 1's complement?
What is the result of removing the radix point before finding 1's complement?
Which statement correctly describes r's complement?
Which statement correctly describes r's complement?
In the context of subtraction using complements, what should be done if A < B?
In the context of subtraction using complements, what should be done if A < B?
How is 2's complement obtained from a binary number with a radix point?
How is 2's complement obtained from a binary number with a radix point?
Which of the following describes diminished radix complement in base r?
Which of the following describes diminished radix complement in base r?
Flashcards
Binary Number System Base
Binary Number System Base
The binary number system uses only two digits: 0 and 1. Its base is 2.
Octal Number System Base
Octal Number System Base
The octal number system uses eight digits: 0 to 7. Its base is 8.
Decimal Representation of (1101)2
Decimal Representation of (1101)2
The decimal equivalent of the binary number 1101 is 13.
Decimal Place Value concept
Decimal Place Value concept
Signup and view all the flashcards
Converting Decimal to Other number system
Converting Decimal to Other number system
Signup and view all the flashcards
r's complement
r's complement
Signup and view all the flashcards
(r-1)'s complement
(r-1)'s complement
Signup and view all the flashcards
1's complement
1's complement
Signup and view all the flashcards
2's complement
2's complement
Signup and view all the flashcards
Subtraction with complements
Subtraction with complements
Signup and view all the flashcards
Study Notes
Number Systems
- Digital circuits rely on binary numbers (0 and 1).
- Decimal number system uses base 10.
- Value of the nth digit from the right = nth digit × (base)n-1.
- Binary number system uses base 2 (0 and 1).
- Octal number system uses base 8 (0-7).
- Hexadecimal number system uses base 16 (0-9, A-F).
Conversion Between Number Systems
- Decimal to binary: Successive division by 2.
- Remainders form the binary number.
- Binary to decimal: Multiply each bit by 2n-1.
- Decimal to octal: Successive division by 8.
- Octal to decimal: Multiply each digit by 8n-1.
- Decimal to hexadecimal: Successive division by 16.
- Hexadecimal to decimal: Multiply each digit by 16n-1.
- Binary to octal: Group binary digits in sets of 3, starting from the right, and replace with corresponding octal digit.
- Octal to binary: Replace each octal digit with its 3-bit binary equivalent.
- Binary to hexadecimal: Group binary digits in sets of 4, starting from the right, and replace with corresponding hexadecimal digit.
- Hexadecimal to binary: Replace each hexadecimal digit with its 4-bit binary equivalent.
Complements
- r's complement: rm - N
- (r-1)'s complement: (rm - 1) - N (where m is the number of digits)
- Useful for subtraction by adding the complement.
- In binary, 1's complement flips 0s to 1s and 1s to 0s; 2's complement adds 1 to the 1's complement.
- End-around carry: if the carryout to the most significant digit is needed, add it to the least significant digit.
Signed Number Representation
- Sign-magnitude: Leftmost bit is the sign, remaining bits are the magnitude.
- 1's complement: Representing a negative number by flipping the bits of its positive representation
- 2's complement: Represent a negative number by taking the 1's complement and adding 1. Common in computers.
Other Topics
- Numeric Codes: Used for representing numbers and non-numerical values in binary, including weighted and non-weighted codes.
- Error detecting and correcting codes: Codes include parity codes.
- Sequential codes: Successive codes differ by one bit.
- Cyclic codes: Codes where successive code words differ by a single bit.
- Reflective codes: In which the nth code words are mirror images of the code words from 0 to n-1 (e.g., Gray codes).
- Self-complementing codes: Codes that can be inverted to represent the complement of the original number's representation.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
