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Questions and Answers
What is the result of adding -46 and -25 using signed magnitude binary arithmetic?
What is the result of adding -46 and -25 using signed magnitude binary arithmetic?
- -71 (correct)
- 25
- -25
- 71
What is a key disadvantage of signed magnitude representation in computer systems?
What is a key disadvantage of signed magnitude representation in computer systems?
- It adds complexity to arithmetic operations. (correct)
- It can only represent positive values.
- It simplifies hardware implementation.
- It allows only one representation for zero.
In one’s complement representation, how is negative 3 expressed in 8-bit binary?
In one’s complement representation, how is negative 3 expressed in 8-bit binary?
- 11111100 (correct)
- 00000011
- 11111101
- 00000000
What is the effect of the carry bit in one’s complement addition?
What is the effect of the carry bit in one’s complement addition?
In signing magnitude binary arithmetic, what happens when the signs of two numbers differ?
In signing magnitude binary arithmetic, what happens when the signs of two numbers differ?
Why do computer systems prefer complement systems over signed magnitude representation?
Why do computer systems prefer complement systems over signed magnitude representation?
What is a result of using one’s complement representation regarding zero?
What is a result of using one’s complement representation regarding zero?
When adding the values 48 and -19 in one’s complement, how is -19 represented?
When adding the values 48 and -19 in one’s complement, how is -19 represented?
What is the result of converting the octal number (736.4) to decimal?
What is the result of converting the octal number (736.4) to decimal?
In binary, what is the decimal equivalent of the number (110.111)?
In binary, what is the decimal equivalent of the number (110.111)?
What is the correct method for converting a decimal fraction to a base R number?
What is the correct method for converting a decimal fraction to a base R number?
Which of the following represents the hexadecimal number for decimal 13?
Which of the following represents the hexadecimal number for decimal 13?
When converting from binary to decimal, what does the binary digit in the 1's place represent?
When converting from binary to decimal, what does the binary digit in the 1's place represent?
What is the base-2 (binary) representation of the decimal number 10?
What is the base-2 (binary) representation of the decimal number 10?
Which numeral system uses the base value of 16?
Which numeral system uses the base value of 16?
In converting the decimal number 54 to binary, which of the following is one of the steps involved?
In converting the decimal number 54 to binary, which of the following is one of the steps involved?
How do you represent a positive number in two’s complement?
How do you represent a positive number in two’s complement?
What is the resulting two’s complement representation of -3 in 8 bits?
What is the resulting two’s complement representation of -3 in 8 bits?
What indicates an overflow condition in signed two’s complement arithmetic?
What indicates an overflow condition in signed two’s complement arithmetic?
In two’s complement arithmetic, how are binary numbers added?
In two’s complement arithmetic, how are binary numbers added?
What is the two’s complement representation of -19 in 8 bits?
What is the two’s complement representation of -19 in 8 bits?
What happens when an overflow occurs in signed number representation?
What happens when an overflow occurs in signed number representation?
Which of the following statements about carry and overflow is true?
Which of the following statements about carry and overflow is true?
What should be done to find the one’s complement of a binary number?
What should be done to find the one’s complement of a binary number?
What is the primary operation involved in arithmetic subtraction using 2's complement?
What is the primary operation involved in arithmetic subtraction using 2's complement?
In floating point representation, what does the exponent signify?
In floating point representation, what does the exponent signify?
Which of the following statements about signed integer representation is correct?
Which of the following statements about signed integer representation is correct?
When performing binary addition, what does the rule '1 + 1 = 10' indicate?
When performing binary addition, what does the rule '1 + 1 = 10' indicate?
What is the significance of the mantissa in floating point representation?
What is the significance of the mantissa in floating point representation?
How is the sum of two numbers calculated using signed magnitude binary arithmetic?
How is the sum of two numbers calculated using signed magnitude binary arithmetic?
Which of the following is NOT part of the binary addition rules?
Which of the following is NOT part of the binary addition rules?
What is the outcome of the operation (±A) - B in 2's complement?
What is the outcome of the operation (±A) - B in 2's complement?
What component of a floating point number representation directly follows the sign bit?
What component of a floating point number representation directly follows the sign bit?
Which of the following statements is true regarding the representation of zero in floating point numbers?
Which of the following statements is true regarding the representation of zero in floating point numbers?
What is the main reason for using internal representation in computing?
What is the main reason for using internal representation in computing?
What does the most significant position of the mantissa represent in floating point numbers?
What does the most significant position of the mantissa represent in floating point numbers?
How are external representations of numbers converted for presentability?
How are external representations of numbers converted for presentability?
What is the purpose of a unified floating point number representation in a computer?
What is the purpose of a unified floating point number representation in a computer?
What distinguishes external representation from internal representation in computing?
What distinguishes external representation from internal representation in computing?
In the binary coded decimal (BCD) system, how is the decimal number 5 represented?
In the binary coded decimal (BCD) system, how is the decimal number 5 represented?
In a 16-bit floating point number representation, how many bits are allocated to the exponent?
In a 16-bit floating point number representation, how many bits are allocated to the exponent?
What is implied in a floating point number representation regarding the radix point?
What is implied in a floating point number representation regarding the radix point?
Study Notes
Representation of Numbers
- Positional Number System: Represents numbers using a base (radix) and place value.
- Common Bases: Decimal (R=10), Binary (R=2), Octal (R=8), Hexadecimal (R=16)
- Decimal, Binary, Octal, Hexadecimal: Represent numbers using different bases with corresponding symbols.
- Conversion between Bases:
- Base R to Decimal: V(A) = S ak Rk, where A is the number, ak is the digit at position k, and R is the base.
- Decimal to Base R:
- Integer Part: Successive divisions by R, collecting remainders.
- Fractional Part: Successive multiplications by R, collecting integer parts.
Fixed Point Representations
- Arithmetic Subtraction in 2’s complement: Compute (A) - (B) as (A) + (-B), where (-B) is the two’s complement of B.
Floating Point Representation
- Floating Point Number: Represents numbers with a mantissa (signed fixed-point) and an exponent.
- Value Representation: V(F) = V(M) * RV(E), where F is the floating-point number, M is the mantissa, E is the exponent, and R is the radix.
Signed Integer Representation
- Binary Addition: Simple rules for adding binary numbers.
- Signed Magnitude: Represents numbers with a sign bit and a magnitude.
- Disadvantage: Two representations for zero (positive and negative).
- One's Complement: Represents negative numbers by inverting all bits of the positive counterpart.
- Disadvantage: Two representations for zero.
- Two's Complement: Represents negative numbers by inverting all bits and adding 1 to the one's complement.
- Advantage: Single representation for zero.
- Detecting Overflow: In two's complement, overflow occurs when the carry-in and carry-out of the sign bit differ.
External Representations
- Internal Representation: Efficient representation for internal calculations.
- External Representation: Human-readable representation for output.
- BCD (Binary Coded Decimal): Represents decimal digits using 4-bit binary codes.
Internal vs. External Representation
- Numbers: Often require internal representation for efficiency and external representation for presentability.
- Alphabets, Symbols, Numbers: Often do not require internal representation as they are not directly involved in calculations.
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Description
This quiz explores the different systems of representing numbers, including positional number systems like decimal, binary, octal, and hexadecimal. It also covers conversion methods between these bases and introduces fixed-point representations and floating-point numbers. Test your understanding of these fundamental concepts in computer science!
