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Questions and Answers
What is the binary representation of the exponent E when converting the number 0.000000110110100101 to IEEE 754 format?
What is the binary representation of the exponent E when converting the number 0.000000110110100101 to IEEE 754 format?
In the IEEE 754 format for the number 0.000000110110100101, what is the sign bit?
In the IEEE 754 format for the number 0.000000110110100101, what is the sign bit?
How many zeros are added to the fraction part when converting the number to IEEE 754 format?
How many zeros are added to the fraction part when converting the number to IEEE 754 format?
What does the equation E - 127 = -7 represent in the context of converting to IEEE 754 format?
What does the equation E - 127 = -7 represent in the context of converting to IEEE 754 format?
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What is the common binary code representation used for decimal digits in internal arithmetic computations?
What is the common binary code representation used for decimal digits in internal arithmetic computations?
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What does control information represent in a computer's memory or processor registers?
What does control information represent in a computer's memory or processor registers?
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Which of the following is NOT a digit in the decimal number system?
Which of the following is NOT a digit in the decimal number system?
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What is the decimal equivalent of the binary number (101101)2?
What is the decimal equivalent of the binary number (101101)2?
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Which radix system is represented by the symbols 0-7?
Which radix system is represented by the symbols 0-7?
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Which are the symbols used in the hexadecimal number system?
Which are the symbols used in the hexadecimal number system?
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When converting from radix r to decimal, what is the process used?
When converting from radix r to decimal, what is the process used?
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In a binary number system, how many distinct symbols are used?
In a binary number system, how many distinct symbols are used?
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Which of the following correctly identifies the components of a number system of base r?
Which of the following correctly identifies the components of a number system of base r?
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What is r’s complement of a number N?
What is r’s complement of a number N?
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What indicates that an overflow has occurred when adding two binary numbers?
What indicates that an overflow has occurred when adding two binary numbers?
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Which of the following statements about floating-point binary representation is true?
Which of the following statements about floating-point binary representation is true?
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How do you convert a binary number such as (10.01101)2 to decimal?
How do you convert a binary number such as (10.01101)2 to decimal?
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What occurs when the addition of two n-digit numbers results in n + 1 digits?
What occurs when the addition of two n-digit numbers results in n + 1 digits?
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If the binary addition of two positive numbers results in a negative outcome, what can be inferred?
If the binary addition of two positive numbers results in a negative outcome, what can be inferred?
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Which of the following describes a component of binary representation?
Which of the following describes a component of binary representation?
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What would be the decimal value of the binary number (00110101)2?
What would be the decimal value of the binary number (00110101)2?
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What does the left-most bit in Signed-Magnitude representation indicate?
What does the left-most bit in Signed-Magnitude representation indicate?
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What is the BCD representation for the decimal number 9?
What is the BCD representation for the decimal number 9?
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In signed-magnitude arithmetic, what must you do if the signs of the two operands differ?
In signed-magnitude arithmetic, what must you do if the signs of the two operands differ?
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Which binary code uses 7 bits to represent 128 characters?
Which binary code uses 7 bits to represent 128 characters?
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What is the mathematical range of integers represented in N-bits using Signed-Magnitude?
What is the mathematical range of integers represented in N-bits using Signed-Magnitude?
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What characterizes an Overflow in signed numbers during arithmetic operations?
What characterizes an Overflow in signed numbers during arithmetic operations?
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What is one limitation of both ASCII and EBCDIC?
What is one limitation of both ASCII and EBCDIC?
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Which method is used for simplifying subtraction operations in digital computers?
Which method is used for simplifying subtraction operations in digital computers?
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How many bits does Unicode use to encode a majority of the world's characters?
How many bits does Unicode use to encode a majority of the world's characters?
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How are the ranges of integers represented in radix r systems defined?
How are the ranges of integers represented in radix r systems defined?
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Which of the following best describes BCD?
Which of the following best describes BCD?
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What operation is primarily simplified by using complements in binary systems?
What operation is primarily simplified by using complements in binary systems?
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What is the basic principle when performing addition in Signed-Magnitude if both signs are the same?
What is the basic principle when performing addition in Signed-Magnitude if both signs are the same?
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What does EBCDIC stand for?
What does EBCDIC stand for?
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Which of the following statements about Unicode is true?
Which of the following statements about Unicode is true?
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What is the purpose of the sign bit in IEEE Standard 754 floating-point formats?
What is the purpose of the sign bit in IEEE Standard 754 floating-point formats?
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In the equation for single-precision floating-point representation, what does 'E' represent?
In the equation for single-precision floating-point representation, what does 'E' represent?
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What is the decimal value of the exponent E for the binary value 10101101?
What is the decimal value of the exponent E for the binary value 10101101?
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Which condition represents positive infinity in IEEE Standard 754 representation?
Which condition represents positive infinity in IEEE Standard 754 representation?
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What is the binary result after converting the single-precision IEEE Standard 754 number 11010110101101101011000000000000?
What is the binary result after converting the single-precision IEEE Standard 754 number 11010110101101101011000000000000?
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How is the binary point positioned in the IEEE floating-point representation?
How is the binary point positioned in the IEEE floating-point representation?
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In creating the IEEE Standard 754 representation, what exponent is used when the decimal point is moved seven positions to the right?
In creating the IEEE Standard 754 representation, what exponent is used when the decimal point is moved seven positions to the right?
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Which of the following conditions represents zero in IEEE Standard 754 representation?
Which of the following conditions represents zero in IEEE Standard 754 representation?
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Study Notes
Number Systems and Codes
- Data types in computer memory and registers include: numbers for arithmetic, letters for processing, and other discrete symbols.
- A number system with base r (radix r) uses r distinct symbols or digits.
- The decimal system (radix 10) uses digits 0 through 9.
- The binary system (radix 2) uses digits 0 and 1.
- The octal system (radix 8) uses digits 0 through 7.
- The hexadecimal system (radix 16) uses digits 0 through 9 and letters A through F.
Number System Conversions
- Decimal to other systems: Separate the integer and fractional parts, convert each part individually. For integers, successive divisions by the desired radix and accumulating remainders are used. For fractions, successive multiplications by the radix and accumulating integer parts are used.
- Other systems to decimal: Use the weighted sum method. Each digit is multiplied by the corresponding power of the radix and all results are summed. For example, (736.4)8 = (7 * 82) + (3 * 81) + (6 * 80) + (4 * 8-1) = 478.510
Signed-Integer Representation
- Methods for representing signed integers in computers:
- Signed-magnitude: The leftmost bit represents the sign (0 for positive, 1 for negative), and the remaining bits represent the magnitude.
- r-1's complement: Used for simplifying subtraction. The (r-1)'s complement of a number N, in base r with n digits, is (r^n - 1) - N
- r's complement: rn-N if N is not zero, 0 if N is zero
- Overflow: Occurs when the result of an arithmetic operation is larger or smaller than the maximum or minimum value that can be represented in the given format.
Complements
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(r-1)'s complement: The result of subtracting a number from the largest representable number in a system (1's complement if base 2)
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r's complement: The result of adding 1 to the (r-1)'s complement.
Floating-Point Binary
- Floating-point numbers represent real numbers using an exponent and fractional part (mantissa) to accommodate vast ranges of values.
- The IEEE 754 standard is a common way to represent floating-point numbers in computers. The standard defines single-precision (32-bit) and double-precision (64-bit) formats.
Other Binary Codes
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Alphanumeric representation codes:
- ASCII (American Standard Code for Information Interchange): 7-bit code, widely used
- EBCDIC (Extended Binary Coded Decimal Interchange Code): 8-bit code, less common
- Unicode: A wider character encoding system capable of dealing with a much bigger set of characters. 16 bits/character, designed to deal with multiple languages.
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BCD (Binary Coded Decimal): Each decimal digit is represented by its binary equivalent, e.g. "0" as "0000", "1" as "0001. Four bits per digit.
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Description
Test your understanding of number systems and their conversions. This quiz covers key concepts including binary, decimal, octal, and hexadecimal systems, as well as methods for converting between them. Challenge yourself and reinforce your knowledge in computer science!