Podcast
Questions and Answers
What is the octal representation of the decimal number (175)10?
What is the octal representation of the decimal number (175)10?
Which of the following binary numbers converts to octal as (26.2)8?
Which of the following binary numbers converts to octal as (26.2)8?
What is the hexadecimal equivalent of the binary number (101101.01)2?
What is the hexadecimal equivalent of the binary number (101101.01)2?
Convert the octal number (62.3)8 to hexadecimal.
Convert the octal number (62.3)8 to hexadecimal.
Signup and view all the answers
If a binary number is (10100110.11)2, what would be the octal representation?
If a binary number is (10100110.11)2, what would be the octal representation?
Signup and view all the answers
What is the decimal equivalent of the binary number (1101110)2?
What is the decimal equivalent of the binary number (1101110)2?
Signup and view all the answers
What is the range of hexadecimal values spanned by digits 0 to 9 in ASCII?
What is the range of hexadecimal values spanned by digits 0 to 9 in ASCII?
Signup and view all the answers
In ASCII, how many bits are used to represent graphic printing characters?
In ASCII, how many bits are used to represent graphic printing characters?
Signup and view all the answers
Which non-printing character is used for record marking and flow control in ASCII?
Which non-printing character is used for record marking and flow control in ASCII?
Signup and view all the answers
What is the purpose of a parity bit in ASCII?
What is the purpose of a parity bit in ASCII?
Signup and view all the answers
Which binary-to-hexadecimal conversion rule is mentioned in the text for translating lowercase to uppercase ASCII characters?
Which binary-to-hexadecimal conversion rule is mentioned in the text for translating lowercase to uppercase ASCII characters?
Signup and view all the answers
In ASCII, what value range do uppercase letters A-Z span in hexadecimal?
In ASCII, what value range do uppercase letters A-Z span in hexadecimal?
Signup and view all the answers
What is the base of the hexadecimal number system?
What is the base of the hexadecimal number system?
Signup and view all the answers
In binary, what is the value of (1011)2 in decimal?
In binary, what is the value of (1011)2 in decimal?
Signup and view all the answers
What is the equivalent of (1100)2 in octal?
What is the equivalent of (1100)2 in octal?
Signup and view all the answers
What is the sum of the binary numbers (1010)2 and (111)2?
What is the sum of the binary numbers (1010)2 and (111)2?
Signup and view all the answers
What is the decimal value of the octal number (232)8?
What is the decimal value of the octal number (232)8?
Signup and view all the answers
Convert the binary number (100110)2 to hexadecimal.
Convert the binary number (100110)2 to hexadecimal.
Signup and view all the answers
What is the binary representation of the decimal number 29?
What is the binary representation of the decimal number 29?
Signup and view all the answers
Convert the octal number (75)8 to hexadecimal.
Convert the octal number (75)8 to hexadecimal.
Signup and view all the answers
'101011' in binary is equivalent to which octal number?
'101011' in binary is equivalent to which octal number?
Signup and view all the answers
'C7' in hexadecimal is equal to which binary number?
'C7' in hexadecimal is equal to which binary number?
Signup and view all the answers
Study Notes
Binary Values
- Binary values are represented abstractly by digits 0 and 1, words (symbols) False (F) and True (T), words (symbols) Low (L) and High (H), and words On and Off
- Binary values are represented by values or ranges of values of physical quantities, such as V(t) Logic 1 undefine and Logic 0 t
Number Systems
- Decimal Number System:
- Base (radix) = 10
- 10 digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
- Digit Position: Integer & fraction
- Digit Weight: Weight = (Base) Position Magnitude
- Sum of “Digit x Weight” Formal Notation: 500 d2B2+d1B1+d0B0+d-1B-1+d-2*B-2
- Octal Number System:
- Base = 8
- 8 digits: {0, 1, 2, 3, 4, 5, 6, 7}
- Weights: Weight = (Base) Position Magnitude
- Sum of “Digit x Weight” Formal Notation: 8 1 1/8 1/64
- Binary Number System:
- Base = 2
- 2 digits: {0, 1}, called binary digits or “bits”
- Weights: Weight = (Base) Position Magnitude
- Sum of “Bit x Weight” Formal Notation: 2 1 1/2 1/4
- Hexadecimal Number System:
- Base = 16
- 16 digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
- Weights: Weight = (Base) Position Magnitude
- Sum of “Digit x Weight” Formal Notation: 256 16 1 1/16 1/256
The Power of 2
- 2n n 2n
- Examples:
- 2^0 = 1
- 2^1 = 2
- 2^2 = 4
- ...
- 2^20 = 1 Mega (M)
- 2^30 = 1 Giga (G)
- 2^40 = 1 Tera (T)
Addition and Subtraction
- Decimal Addition:
- 1 + 1 = 1 Carry
- Example: 5 + 5 = 10
- Binary Addition:
- Column Addition
- Example: 1 + 1 = 10
- Binary Subtraction:
- Borrow a “Base” when needed
- Example: 0 - 1 = 1 (borrowing 1)
Binary Multiplication
- Bit by bit
- Example: 1 x 1 = 1
Number Base Conversions
- Evaluate Magnitude:
- Octal (Base 8)
- Decimal (Base 10)
- Binary (Base 2)
- Hexadecimal (Base 16)
- Conversion Examples:
- Decimal (Integer) to Binary Conversion
- Decimal (Fraction) to Binary Conversion
- Binary to Octal Conversion
- Binary to Hexadecimal Conversion
- Octal to Hexadecimal Conversion
ASCII Codes
- American Standard Code for Information Interchange (ASCII)
- Character Code
- 7-bit code to represent:
- 94 Graphic printing characters
- 34 Non-printing characters
- ASCII Properties:
- Digits 0 to 9 span Hexadecimal values 30 to 39
- Upper case A-Z span 41 to 5A
- Lower case a-z span 61 to 7A
- Lower to upper case translation (and vice versa) occurs by flipping bit 6
Binary Codes
- Error-Detecting Code:
- Adding an eighth bit to the ASCII character to indicate its parity
- Parity bit is an extra bit included with a message to make the total number of 1's either even or odd
Complements
- Two types of complements for each base-r system:
- Radix complement
- Diminished radix complement
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers topics such as converting fractions to binary, decimal to octal, and binary to octal. It includes examples with step-by-step solutions for better understanding.
