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Questions and Answers
Why are number systems considered the language of computers?
Why are number systems considered the language of computers?
- Because computers perform calculations using these systems. (correct)
- Because all computer programs are written in number systems.
- Because numbers systems are the only way to store data.
- Because humans communicate with computers using numbers.
What is the base of the octal number system?
What is the base of the octal number system?
- 10
- 16
- 8 (correct)
- 2
Which number system is most closely associated with digital systems?
Which number system is most closely associated with digital systems?
- Binary (correct)
- Hexadecimal
- Decimal
- Octal
What does a 'bit' represent in the context of binary numbers?
What does a 'bit' represent in the context of binary numbers?
Why is the hexadecimal (base-16) system often used in computing?
Why is the hexadecimal (base-16) system often used in computing?
In the decimal number 953, how is the value determined using powers of 10?
In the decimal number 953, how is the value determined using powers of 10?
What is the decimal equivalent of the binary number 11010?
What is the decimal equivalent of the binary number 11010?
What decimal value does the binary number 111 represent?
What decimal value does the binary number 111 represent?
If a number in the octal system is represented as "10", what would be its equivalent in the decimal system?
If a number in the octal system is represented as "10", what would be its equivalent in the decimal system?
What is the decimal equivalent of the octal number 23?
What is the decimal equivalent of the octal number 23?
What is the largest possible number that can be represented using a single digit in hexadecimal?
What is the largest possible number that can be represented using a single digit in hexadecimal?
What decimal value does the hexadecimal digit 'A' represent?
What decimal value does the hexadecimal digit 'A' represent?
What is the next number in hexadecimal after '9'?
What is the next number in hexadecimal after '9'?
What is the maximum number that can be represented with two digits in base 16?
What is the maximum number that can be represented with two digits in base 16?
What is the equivalent of decimal 15 in hexadecimal?
What is the equivalent of decimal 15 in hexadecimal?
What is the result of subtracting 1 from 10 (decimal) in binary?
What is the result of subtracting 1 from 10 (decimal) in binary?
What arithmetic operation is primarily used in converting a decimal number to binary?
What arithmetic operation is primarily used in converting a decimal number to binary?
What should you do with the integer part of each multiplication result when converting a decimal fraction to binary?
What should you do with the integer part of each multiplication result when converting a decimal fraction to binary?
In converting a number with a fractional part from decimal to binary, what determines when to stop the multiplication process for the fractional part?
In converting a number with a fractional part from decimal to binary, what determines when to stop the multiplication process for the fractional part?
When converting from decimal to binary using division, in what order should the remainders be written to obtain the correct binary number?
When converting from decimal to binary using division, in what order should the remainders be written to obtain the correct binary number?
What binary digits correspond to 27 in decimal?
What binary digits correspond to 27 in decimal?
When converting the decimal number 28 into binary using successive divisions by 2, what is the correct binary representation?
When converting the decimal number 28 into binary using successive divisions by 2, what is the correct binary representation?
What is the binary equivalent of octal 7?
What is the binary equivalent of octal 7?
What is the octal representation of the binary number 010 110 001?
What is the octal representation of the binary number 010 110 001?
What is the first step in converting a binary number to its hexadecimal representation?
What is the first step in converting a binary number to its hexadecimal representation?
What single hexadecimal digit is equivalent to the binary number 1011?
What single hexadecimal digit is equivalent to the binary number 1011?
What is the binary equivalent of hexadecimal 'D'?
What is the binary equivalent of hexadecimal 'D'?
What is the hexadecimal equivalent of the binary number 0011 0000 0110?
What is the hexadecimal equivalent of the binary number 0011 0000 0110?
If you have the hexadecimal number 306.D, what is its equivalent in binary?
If you have the hexadecimal number 306.D, what is its equivalent in binary?
Which of the following is an example of a number that includes both integer and fractional parts?
Which of the following is an example of a number that includes both integer and fractional parts?
Which of the following statements accurately describes the process of converting decimal numbers with both integer and fraction parts into binary?
Which of the following statements accurately describes the process of converting decimal numbers with both integer and fraction parts into binary?
In a number system, what digits from octal represent with binary systems from left to right?
In a number system, what digits from octal represent with binary systems from left to right?
If you are converting decimal 41.6875 to binary, which of the following best describes what Step-1 and Step-2 consist of?
If you are converting decimal 41.6875 to binary, which of the following best describes what Step-1 and Step-2 consist of?
If you are converting number 41.6875 to binary, what method should you use in order to have a right response?
If you are converting number 41.6875 to binary, what method should you use in order to have a right response?
In the binary number system, what does the term 'MSB' stand for?
In the binary number system, what does the term 'MSB' stand for?
Given the binary number 11001100, which bit is the MSB?
Given the binary number 11001100, which bit is the MSB?
In the context of binary numbers, what is the significance of the 'Most Significant Bit' (MSB)?
In the context of binary numbers, what is the significance of the 'Most Significant Bit' (MSB)?
How does the positional value of each bit change as you move from the rightmost bit to the leftmost bit in a binary number?
How does the positional value of each bit change as you move from the rightmost bit to the leftmost bit in a binary number?
Which of the following binary numbers represents the decimal number 41?
Which of the following binary numbers represents the decimal number 41?
What is the result of adding the binary numbers 1010 and 0110?
What is the result of adding the binary numbers 1010 and 0110?
What values does the octal system use?
What values does the octal system use?
If the result is greater than 7 for an equation in octal, what do you do?
If the result is greater than 7 for an equation in octal, what do you do?
Convert octal 77 to decimal.
Convert octal 77 to decimal.
What is the decimal representation of the octal number 11?
What is the decimal representation of the octal number 11?
What values does the hexadecimal system use?
What values does the hexadecimal system use?
What is the decimal equivalent of the hexadecimal number '10'?
What is the decimal equivalent of the hexadecimal number '10'?
What is the hexadecimal equivalent of the decimal number 200?
What is the hexadecimal equivalent of the decimal number 200?
What is the main operation to convert from decimal to binary numbers?
What is the main operation to convert from decimal to binary numbers?
Which of the following steps is part of converting a decimal number (integer) to binary?
Which of the following steps is part of converting a decimal number (integer) to binary?
In what order are the remainders written to obtain the correct binary number?
In what order are the remainders written to obtain the correct binary number?
If you are converting decimal 63 to binary, what first five steps look like?
If you are converting decimal 63 to binary, what first five steps look like?
When converting decimal 45 into binary using successive divisions by 2, what binary representation best describes this?
When converting decimal 45 into binary using successive divisions by 2, what binary representation best describes this?
Which statement is true regarding the conversion of a decimal number with both integer and fractional parts into binary?
Which statement is true regarding the conversion of a decimal number with both integer and fractional parts into binary?
If you have the number 123.45 adn you are going to convert it to the binary, what methods will you use?
If you have the number 123.45 adn you are going to convert it to the binary, what methods will you use?
What binary value will octal digit 5 present, from left to right?
What binary value will octal digit 5 present, from left to right?
Converting number 67.78 to binary requires what methods?
Converting number 67.78 to binary requires what methods?
When converting from decimal 11011 to hexadecimal number A11, what is the last number to use?
When converting from decimal 11011 to hexadecimal number A11, what is the last number to use?
14/2 gives remainder = 0 in the first step, what steps would follow up?
14/2 gives remainder = 0 in the first step, what steps would follow up?
Given the binary number 101111, what do you do to see it in a result of decimal?
Given the binary number 101111, what do you do to see it in a result of decimal?
Given the binary number 111111, how do you decrement value from the right, increment power, stop, and add all ?
Given the binary number 111111, how do you decrement value from the right, increment power, stop, and add all ?
With binary number 1111, and decimal power going from 0,1,2 what is missing?
With binary number 1111, and decimal power going from 0,1,2 what is missing?
If you have binary number 100101 going to any number system, and start from right, and use power 0, what would be the next step?
If you have binary number 100101 going to any number system, and start from right, and use power 0, what would be the next step?
You dividing from decimal (going to low) by high system (binary), and remainders look like [10110] when going from bottom to top, so from top to bottom you will?
You dividing from decimal (going to low) by high system (binary), and remainders look like [10110] when going from bottom to top, so from top to bottom you will?
If the decimal is (64)10, we will have (1000000)2 result, however from each step you write down reminder bottom to top, you?
If the decimal is (64)10, we will have (1000000)2 result, however from each step you write down reminder bottom to top, you?
If you have the binary 111 with octal, what does 1 best present it?
If you have the binary 111 with octal, what does 1 best present it?
You take digits and divide/ multiplication by to the destination, with remainders and values on paper?
You take digits and divide/ multiplication by to the destination, with remainders and values on paper?
If the base looks like 'XXX' number and decimal is smaller, you are?
If the base looks like 'XXX' number and decimal is smaller, you are?
When converting the decimal number 153 to octal, what are the intermediate steps and the final result?
When converting the decimal number 153 to octal, what are the intermediate steps and the final result?
What is the result of converting the binary number 010110001101011.11110010 to octal?
What is the result of converting the binary number 010110001101011.11110010 to octal?
What are the initial steps for converting the decimal number 245 to hexadecimal?
What are the initial steps for converting the decimal number 245 to hexadecimal?
If the remainders after dividing 245 by 16 are 5 and 15 (in that order), what is the hexadecimal representation of the decimal number 245?
If the remainders after dividing 245 by 16 are 5 and 15 (in that order), what is the hexadecimal representation of the decimal number 245?
What is the binary representation of the Octal number 306.7?
What is the binary representation of the Octal number 306.7?
Flashcards
Decimal Number System
Decimal Number System
The number system we use everyday, with base 10.
Binary Number System
Binary Number System
A base-2 number system using 0 and 1, fundamental in digital systems.
Octal Number System
Octal Number System
A base-8 number system, shorthand notation for binary.
Hexadecimal Number System
Hexadecimal Number System
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Bit (Binary Digit)
Bit (Binary Digit)
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Most Significant Bit (MSB)
Most Significant Bit (MSB)
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Least Significant Bit (LSB)
Least Significant Bit (LSB)
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Binary to Decimal Conversion
Binary to Decimal Conversion
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Decimal to Binary Conversion
Decimal to Binary Conversion
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Decimal to Binary (with Fraction)
Decimal to Binary (with Fraction)
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Binary to Octal Conversion
Binary to Octal Conversion
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Binary to Hex Conversion
Binary to Hex Conversion
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Octal to Binary Conversion
Octal to Binary Conversion
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Hex to Binary Conversion
Hex to Binary Conversion
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Study Notes
- Number Systems play a crucial role as the language of computers.
Different Number Systems:
- Decimal (Base 10) is the everyday number system.
- Binary (Base 2) is used in digital systems.
- Octal (Base 8) is a shorthand for binary representation.
- Hexadecimal (Base 16) represents binary in a compact form.
Decimal Numbers:
- Decimal numbers is the Number with base 10
- To convert decimal numbers, each digit is multiplied by the appropriate power of 10.
- For example, 953 in base 10 can be expressed as (9 * 10^2) + (5 * 10^1) + (3 * 10^0).
Binary Numbers:
- A binary digit is known as a bit.
- Binary, uses a system of arithmetic with two logic states: 0 and 1.
- Binary numbers are a base-2 numeral system.
- Only the digits 0 and 1 are used.
- The right most bit is the Least Significant Bit (LSB).
- The left most bit is the Most Significant Bit (MSB).
Octal Numbers:
- In the octal system, the base is eight and each place is a power of eight.
- Digits 0-7 are the only ones used.
- The decimal number 8 equals 10 in octal.
- The decimal number 9 is represented as 11 in octal.
Hexadecimal Numbers:
- There are 16 symbols used in the hexadecimal system, 0-9 and A-F.
- Symbols 0-9 represent corresponding numerals in the decimal system and symbols A-F represent decimal values 10-15.
- The hexadecimal system is also called base-16.
Number Conversions:
- Number conversions include Binary to Decimal, Decimal to Binary, Decimal to Octal, and Decimal to Hex.
- Conversions also exist for numbers with fractions like, Decimal to Binary, Binary to octal, Binary to Hex, Octal to Binary, and Hex to Binary.
- Formula: Maximum number = n-1:
- Decimal is 10-1 = 9.
- Binary is 2-1 =1.
- Octal is 8-1 = 7.
- Hexadecimal is 16-1 =15 = F
Binary to Decimal:
- Binary numbers are converted to decimal numbers by using xxxx in base 2 becoming yyyy in base 10.
- Multiply each binary digit by the appropriate power of 2.
- Can convert from base-2 to base-10.
Decimal to Binary:
- Convert decimal numbers to binary numbers where XXXX in base 10, becomes yyyy in base 2.
- Binary to Decimal Conversion: the the inverse is also true : Multiplications
- Decimal to Binary Conversion, Divisions are used.
Decimal to Octal:
- Base10 turns into Base8.
- Example: 153 base 10 = (?) base 8.
Octal to Binary:
- Conversion from binary to octal
- To preform a conversion split the binary into groups of 3
Binary to Hexadecimal
- Conversion from binary to hexadecimal
- To preform a conversion split the binary into groups of 4
Integer with fraction conversion:
- To convert numbers with both integer and fraction parts into binary, each part needs to be converted separately and combined.
- Steps for Integer Part Conversion: Divide the integer part repeatedly by 2 noting the remainder. Write the remainders in reverse order to get its binary equivalent.
- Steps for Fractional Part Conversion: Multiply the fractional part by 2, repeatedly and note down the integer part (0 or 1) after multiplication.
- Continue until the fraction becomes 0 or the desired precision has been reached
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