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Questions and Answers
What is the first step in converting a decimal number to binary?
How do you obtain the binary equivalent after calculating the remainders?
Which of the following is a valid representation for the decimal number 657 in binary?
What base does the octal number system use?
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In the binary multiplication table, what is the result of 1 multiplied by 1?
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What symbols are used in the hexadecimal number system?
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Which decimal number is equivalent to the hexadecimal symbol 'C'?
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When converting the decimal number 987 to binary, what is the last remainder obtained?
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What is the decimal equivalent of the binary number (1011)2?
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What is the decimal equivalent of the binary number (100110)2?
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When adding the binary numbers (10101)2 and (00111)2, what is the result?
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What is the result of subtracting the binary number (01010)2 from (10011)2?
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What is the product of the binary numbers (101)2 and (011)2?
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What is the result of multiplying (1011)2 by (101)2?
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What is the decimal equivalent of the binary number (10101)2?
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What is the outcome of subtracting (001)2 from (111)2?
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What is the base of the Binary number system?
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Which digits are used in the Hexadecimal number system?
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In Binary subtraction, what is the result of 1 - 1?
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Which of the following statements is true regarding the Decimal number system?
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Who introduced the concept of zero?
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When converting a Decimal number to Binary, by which number is the Decimal number divided?
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In Binary multiplication, what is 1 multiplied by 0?
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What is the significance of the right-most digit in a number?
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Study Notes
Decimal to Binary Conversion
- Divide the decimal number by 2, noting the remainder.
- Continue dividing the quotient by 2 and recording remainders.
- Repeat until the quotient reaches zero.
- Reverse the order of remainders to obtain the binary equivalent.
Binary Multiplication Rules
- Follows the same principles as decimal multiplication.
- Multiplication outcomes:
- 0 * 0 = 0
- 0 * 1 = 0
- 1 * 0 = 0
- 1 * 1 = 0 with a carry of 1.
Octal Number System
- Consists of eight digits: 0 to 7.
- Based on base 8.
- Originated from Native American counting methods using finger spacing.
Hexadecimal Number System
- Comprises 16 symbols: 0-9 and A-F.
- Represents decimal values as follows:
- A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
- Based on base 16.
Decimal to Binary Conversion Examples
- 68 in decimal:
- Binary equivalent is 1000100 (2).
- 987 in decimal:
- Binary equivalent is 1111011011 (2).
- 657 in decimal:
- Binary equivalent is 1010010001 (2).
Binary to Decimal Conversion Examples
- (1011)₂ = 11 (10).
- (100110)₂ = 38 (10).
- (10101)₂ = 21 (10).
Binary Addition Examples
- 10101 + 00111 = 11100.
- 1000101101 + 1001101 = 1001001110.
- 1101 + 1001 = 10110.
Binary Subtraction Examples
- 10011 - 01010 = 01001.
- 11001001 - 01100110 = 11000011.
- 111 - 001 = 110.
Binary Multiplication Examples
- 101 * 011 = 1111.
- 1011 * 101 = 1101111.
- 101010 * 1011 = 111001110.
Recap of Number Systems
- Decimal: Base 10, digits 0-9.
- Binary: Base 2, digits 0-1.
- Octal: Base 8, digits 0-7.
- Hexadecimal: Base 16, digits 0-9 and A-F.
Important Definitions
- Least Significant Digit: Rightmost digit in a number.
- Most Significant Digit: Leftmost digit in a number.
Fill in the Blanks
- The base of the Binary number system is 2.
- The base of the Decimal number system is 10.
- Octal number system uses 8 digits.
- Binary numbers are used by computers.
- Hexadecimal includes 0-9 and A-F.
- In Binary subtraction, 1 - 1 = 0.
True or False Statements
- Arithmetic operations can be performed on binary numbers: False.
- Decimal system involves digits 0 to 9: True.
- Binary division is similar to decimal: False.
- 1 multiplied by 0 equals 0: True.
- Valid digits in Octal range from 1 to 7: False.
Multiple Choice Questions
- Zero was conceptualized by b) Aryabhata.
- C in hexadecimal represents c) 12.
- Computers understand c) Binary code.
- In binary multiplication, 1 * 1 equals b) 1.
- Decimal to binary conversion involves division by a) 2.
Number System Definition
- Represents values for various quantities (e.g., counting, statistics).
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Description
Test your knowledge on converting decimal numbers to binary and other number systems. This quiz covers important concepts such as binary multiplication, octal bases, and hexadecimal symbols. Perfect for students studying number systems in mathematics.
