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Questions and Answers
What is the largest positive number that can be represented using four bits in sign magnitude representation?
What is the largest positive number that can be represented using four bits in sign magnitude representation?
How many additional negative integers can be represented compared to positive integers using n bits?
How many additional negative integers can be represented compared to positive integers using n bits?
What is the two's complement value of the binary number 1111?
What is the two's complement value of the binary number 1111?
If all bits are set to 1 in a four-bit representation, what will be the result?
If all bits are set to 1 in a four-bit representation, what will be the result?
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When performing arithmetic operations in two's complement, what happens if the result goes beyond representable limits?
When performing arithmetic operations in two's complement, what happens if the result goes beyond representable limits?
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In the formula Val = −2^(n−1) * An−1 + ∑(2^i * Ai), what does An−1 signify?
In the formula Val = −2^(n−1) * An−1 + ∑(2^i * Ai), what does An−1 signify?
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Which binary number represents the decimal value -2 in four bits?
Which binary number represents the decimal value -2 in four bits?
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What is the effect of moving clockwise on the 'circle' of representable numbers when adding a positive number?
What is the effect of moving clockwise on the 'circle' of representable numbers when adding a positive number?
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What is the primary function of the leftmost bit in sign/magnitude notation?
What is the primary function of the leftmost bit in sign/magnitude notation?
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What complication arises from having two representations for zero in sign/magnitude notation?
What complication arises from having two representations for zero in sign/magnitude notation?
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Which technique eliminates the issue of having multiple representations for zero?
Which technique eliminates the issue of having multiple representations for zero?
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In the Two's complement system, what is indicated by a sign bit of 1?
In the Two's complement system, what is indicated by a sign bit of 1?
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If a binary number A, represented in Two's complement, has its sign bit as 0, what can be inferred about A?
If a binary number A, represented in Two's complement, has its sign bit as 0, what can be inferred about A?
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How many unique patterns can be represented with m bits in the signed number representation?
How many unique patterns can be represented with m bits in the signed number representation?
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Which of the following statements about sign/magnitude notation is true?
Which of the following statements about sign/magnitude notation is true?
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Which of the following is not a common technique for representing signed numbers?
Which of the following is not a common technique for representing signed numbers?
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What is the decimal equivalent of the octal number 27?
What is the decimal equivalent of the octal number 27?
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What is the result of adding the two's complement values +7 and -2?
What is the result of adding the two's complement values +7 and -2?
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When converting the hexadecimal number 1D to decimal, what number do we get?
When converting the hexadecimal number 1D to decimal, what number do we get?
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What does the carry register store in binary arithmetic?
What does the carry register store in binary arithmetic?
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Which of the following statements is true about binary addition?
Which of the following statements is true about binary addition?
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What is the result of flipping the bits of +5 and adding one to get its two's complement?
What is the result of flipping the bits of +5 and adding one to get its two's complement?
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In binary addition, what happens when you reach a carry from adding 1 and 1?
In binary addition, what happens when you reach a carry from adding 1 and 1?
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When adding two signed binary numbers, what is the significance of the bit in the column to the left of the high order bit?
When adding two signed binary numbers, what is the significance of the bit in the column to the left of the high order bit?
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What is the two’s complement representation of -6 in 4 bits?
What is the two’s complement representation of -6 in 4 bits?
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Which procedure is NOT part of converting a negative decimal number to two’s complement?
Which procedure is NOT part of converting a negative decimal number to two’s complement?
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What is the decimal value of the two’s complement binary 11100?
What is the decimal value of the two’s complement binary 11100?
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When using two’s complement, how many unique values can be represented with 4 bits?
When using two’s complement, how many unique values can be represented with 4 bits?
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If the leftmost bit of a binary number in two’s complement is 0, what can be concluded about the number?
If the leftmost bit of a binary number in two’s complement is 0, what can be concluded about the number?
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Which of the following binary numbers represents the decimal value +7 in two’s complement?
Which of the following binary numbers represents the decimal value +7 in two’s complement?
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What will be the two's complement representation of the decimal number +4 in 4 bits?
What will be the two's complement representation of the decimal number +4 in 4 bits?
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What is a key advantage of using two’s complement for representing integers?
What is a key advantage of using two’s complement for representing integers?
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What is the two's complement representation of -9?
What is the two's complement representation of -9?
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Which of the following indicates an overflow condition during addition in two's complement?
Which of the following indicates an overflow condition during addition in two's complement?
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What is the result of adding 5 and 14 in a 5-bit two's complement system?
What is the result of adding 5 and 14 in a 5-bit two's complement system?
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How do you perform subtraction using two's complement?
How do you perform subtraction using two's complement?
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What is the two's complement of 0?
What is the two's complement of 0?
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What is the result of flipping the bits of the binary number 11011?
What is the result of flipping the bits of the binary number 11011?
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After flipping the bits of 11011 and adding 1, what is the resulting binary number?
After flipping the bits of 11011 and adding 1, what is the resulting binary number?
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When would you not encounter an overflow condition in two's complement addition?
When would you not encounter an overflow condition in two's complement addition?
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Study Notes
Signed Number Representations
- Signed numbers are represented within the same binary digit limits as unsigned numbers, using limited patterns split between positive and negative values.
- Three popular techniques for signed number representation include:
- Sign/Magnitude
- Two's Complement
- Binary Coded Decimal
Sign/Magnitude Notation
- Simplest encoding method for signed numbers where the leftmost bit is the sign bit:
- 0 indicates a positive number.
- 1 indicates a negative number.
- Remaining bits represent the magnitude in unsigned binary.
- Notable issue: Two representations for zero (+0 and -0) can complicate equality checks in computers.
Two’s Complement
- Based on modular arithmetic; uses patterns to represent signed integers.
- Positive values: First bit (sign bit) is 0.
- Negative values: First bit is 1, allowing representation of integers from -1 to -2^(n-1).
- Calculation formula for two’s complement value:
- Val = -2^(n-1) * An-1 + Σ(2^i * Ai) for i=0 to n-2
- Always has a single representation for zero.
Two's Complement Examples
- To represent a negative number:
- Find binary for positive equivalent.
- Flip all bits and add 1.
- Example: To get -5 in 5 bits:
- +5 in binary: 00101 → Flip: 11010 → Add 1: 11011
- Example: To convert binary 11100:
- Flip bits: 00011 → Add 1: 00100 → Result: -4
Arithmetic with Two’s Complement
- Uses a simplified binary addition mechanism:
- A 2x2 addition table suffices for operation.
- Example of adding numbers:
- Adding +5 and +6: 00101 + 00110 = 01011 (11 in decimal).
- Adding +7 and -2 requires flipping bits for -2 before performing addition.
Carry and Overflow
- Extra carry from leftmost addition bit can be disregarded (similar to subtracting the modulus).
- Overflow occurs when adding two positive numbers yields a negative result or two negative numbers yield a positive result.
- Overflow and carry stored in special registers for additional handling and error checking.
Subtraction with Two’s Complement
- Subtraction is performed by adding the two's complement (negation) of the second number:
- D = Y - X becomes D = -X + Y.
- Negation involves flipping bits of X and adding 1 before performing the addition routine.
Summary of Addition Rules
- Result from adding A + B:
- Discard excess carry.
- Store carry and overflow status for further reference.
- Allows for systematic error checking and message integrity in computational processes.
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Description
This quiz covers the concept of signed number representations in binary systems as discussed in CS101. It explores how signed quantities can be represented using a limited number of digits, and the implications of this restriction on binary patterns. Test your understanding of signed versus unsigned representations.
