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The range of signed decimal numbers that can be represented by 6-bit 1's complement number is:
- a)-31 to +31
- b)-63 to +63
- c)-64 to +63
- d)-32 to +31
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The range of signed decimal numbers that can be represented by 6-bit 1...
The Range of Signed Decimal Numbers in 6-bit 1's Complement Representation
In a 6-bit 1's complement representation, the most significant bit (MSB) is used as the sign bit, where 0 represents a positive number and 1 represents a negative number. The remaining 5 bits are used to represent the magnitude of the number. Let's analyze the range of signed decimal numbers that can be represented in this system.
Positive Numbers
In a 6-bit 1's complement representation, a positive number is represented directly as its magnitude using the 5 remaining bits. The range of positive numbers can be determined as follows:
- The smallest positive number that can be represented is when all 5 magnitude bits are 0, resulting in a decimal value of 00000, which represents 0.
- The largest positive number that can be represented is when all 5 magnitude bits are 1, resulting in a decimal value of 11111, which represents 31.
Therefore, the range of positive numbers in a 6-bit 1's complement representation is 0 to 31.
Negative Numbers
In a 6-bit 1's complement representation, a negative number is represented by taking the 1's complement of its magnitude and adding the sign bit. The range of negative numbers can be determined as follows:
- The smallest negative number that can be represented is when all 5 magnitude bits are 1, resulting in a decimal value of 11111, which represents -0. However, in 1's complement representation, -0 is equivalent to +0. Therefore, -0 is not considered a valid negative number.
- The largest negative number that can be represented is when all 5 magnitude bits are 0, resulting in a decimal value of 00000, which represents -31.
Therefore, the range of negative numbers in a 6-bit 1's complement representation is -31 to -1.
Combining Positive and Negative Numbers
Combining the range of positive and negative numbers, we get the overall range of signed decimal numbers that can be represented in a 6-bit 1's complement representation:
- The smallest number that can be represented is -31.
- The largest number that can be represented is 31.
Therefore, the correct answer is option 'A': -31 to 31.
In a 6-bit 1's complement representation, the most significant bit (MSB) is used as the sign bit, where 0 represents a positive number and 1 represents a negative number. The remaining 5 bits are used to represent the magnitude of the number. Let's analyze the range of signed decimal numbers that can be represented in this system.
Positive Numbers
In a 6-bit 1's complement representation, a positive number is represented directly as its magnitude using the 5 remaining bits. The range of positive numbers can be determined as follows:
- The smallest positive number that can be represented is when all 5 magnitude bits are 0, resulting in a decimal value of 00000, which represents 0.
- The largest positive number that can be represented is when all 5 magnitude bits are 1, resulting in a decimal value of 11111, which represents 31.
Therefore, the range of positive numbers in a 6-bit 1's complement representation is 0 to 31.
Negative Numbers
In a 6-bit 1's complement representation, a negative number is represented by taking the 1's complement of its magnitude and adding the sign bit. The range of negative numbers can be determined as follows:
- The smallest negative number that can be represented is when all 5 magnitude bits are 1, resulting in a decimal value of 11111, which represents -0. However, in 1's complement representation, -0 is equivalent to +0. Therefore, -0 is not considered a valid negative number.
- The largest negative number that can be represented is when all 5 magnitude bits are 0, resulting in a decimal value of 00000, which represents -31.
Therefore, the range of negative numbers in a 6-bit 1's complement representation is -31 to -1.
Combining Positive and Negative Numbers
Combining the range of positive and negative numbers, we get the overall range of signed decimal numbers that can be represented in a 6-bit 1's complement representation:
- The smallest number that can be represented is -31.
- The largest number that can be represented is 31.
Therefore, the correct answer is option 'A': -31 to 31.
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The range of signed decimal numbers that can be represented by 6-bit 1...
The 1's complement number is a 6-bit number. We have to find the maximum and minimum number which can be represented by it.
When the number is negative, then the maximum value can be 111111, i.e. -(26 - 1) = (-31)10.
Here, MSB is for sign.
Maximum positive number is 0 11111, i.e. + (26- 1) = (+ 31)10.
Hence, the range of signed decimal numbers that can be represented by 6-bit 1's complement number is: -31 to +31.
When the number is negative, then the maximum value can be 111111, i.e. -(26 - 1) = (-31)10.
Here, MSB is for sign.
Maximum positive number is 0 11111, i.e. + (26- 1) = (+ 31)10.
Hence, the range of signed decimal numbers that can be represented by 6-bit 1's complement number is: -31 to +31.
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