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Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3 ⋅ b2b1b0 where the position of the binary point is between b3 and b2 . Assume b7 is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?
- a)None of (i), (ii), (iii), (iv) can be exactly represented
- b)Only (ii) cannot be exactly represented
- c)Only (iii) and (iv) cannot be exactly represented
- d)Only (i) and (ii) cannot be exactly represented
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the unsigned 8-bit fixed point binary number representation, ...
(i) 31.500 can be represented as : (31.5)10 = (11111.100)2
24 + 23 22 + 21 + 20 + 2-1 = 16 + 8 + 4 + 2 + 1 + 0.5 = (31.05)10
24 + 23 22 + 21 + 20 + 2-1 = 16 + 8 + 4 + 2 + 1 + 0.5 = (31.05)10
(ii) 0.875 can be represented as : (0.875)10 = (00000.111)2
2-1 + 2-2 2-3 = 0.50 + 0.25 + 0.125 = (0.875)10
2-1 + 2-2 2-3 = 0.50 + 0.25 + 0.125 = (0.875)10
(iii) and (iv) can not be be represented. Therefore, option (C) is Correct.
Most Upvoted Answer
Consider the unsigned 8-bit fixed point binary number representation, ...
B2b1b0.
In this representation, the most significant bit (MSB) is b7, and the least significant bit (LSB) is b0. The number can represent values from 0 to 255, where 0 is represented by all zeros (00000000) and 255 is represented by all ones (11111111).
The binary point is located between b3 and b2, so the number can represent values with fractional parts from 0 to 1. The value of each bit position is determined by its weight, with the MSB having the highest weight and the LSB having the lowest weight.
To convert a binary number to its decimal equivalent, you can use the following formula:
Decimal value = (b7 * 2^7) + (b6 * 2^6) + (b5 * 2^5) + (b4 * 2^4) + (b3 * 2^3) + (b2 * 2^2) + (b1 * 2^1) + (b0 * 2^0).
For example, if the binary number is 11010011, the decimal value would be:
Decimal value = (1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (1 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0)
= (128) + (64) + (0) + (16) + (0) + (0) + (2) + (1)
= 211.
In this representation, the most significant bit (MSB) is b7, and the least significant bit (LSB) is b0. The number can represent values from 0 to 255, where 0 is represented by all zeros (00000000) and 255 is represented by all ones (11111111).
The binary point is located between b3 and b2, so the number can represent values with fractional parts from 0 to 1. The value of each bit position is determined by its weight, with the MSB having the highest weight and the LSB having the lowest weight.
To convert a binary number to its decimal equivalent, you can use the following formula:
Decimal value = (b7 * 2^7) + (b6 * 2^6) + (b5 * 2^5) + (b4 * 2^4) + (b3 * 2^3) + (b2 * 2^2) + (b1 * 2^1) + (b0 * 2^0).
For example, if the binary number is 11010011, the decimal value would be:
Decimal value = (1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (1 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0)
= (128) + (64) + (0) + (16) + (0) + (0) + (2) + (1)
= 211.
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Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3⋅ b2b1b0where the position of the binary point is between b3and b2. Assume b7is the most significant bit. Some of the decimal numbers listed belowcannotbe representedexactlyin the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?a)None of (i), (ii), (iii), (iv) can be exactly representedb)Only (ii) cannot be exactly representedc)Only (iii) and (iv) cannot be exactly representedd)Only (i) and (ii) cannot be exactly representedCorrect answer is option 'C'. Can you explain this answer?
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Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3⋅ b2b1b0where the position of the binary point is between b3and b2. Assume b7is the most significant bit. Some of the decimal numbers listed belowcannotbe representedexactlyin the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?a)None of (i), (ii), (iii), (iv) can be exactly representedb)Only (ii) cannot be exactly representedc)Only (iii) and (iv) cannot be exactly representedd)Only (i) and (ii) cannot be exactly representedCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3⋅ b2b1b0where the position of the binary point is between b3and b2. Assume b7is the most significant bit. Some of the decimal numbers listed belowcannotbe representedexactlyin the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?a)None of (i), (ii), (iii), (iv) can be exactly representedb)Only (ii) cannot be exactly representedc)Only (iii) and (iv) cannot be exactly representedd)Only (i) and (ii) cannot be exactly representedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3⋅ b2b1b0where the position of the binary point is between b3and b2. Assume b7is the most significant bit. Some of the decimal numbers listed belowcannotbe representedexactlyin the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?a)None of (i), (ii), (iii), (iv) can be exactly representedb)Only (ii) cannot be exactly representedc)Only (iii) and (iv) cannot be exactly representedd)Only (i) and (ii) cannot be exactly representedCorrect answer is option 'C'. Can you explain this answer?.
Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3⋅ b2b1b0where the position of the binary point is between b3and b2. Assume b7is the most significant bit. Some of the decimal numbers listed belowcannotbe representedexactlyin the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?a)None of (i), (ii), (iii), (iv) can be exactly representedb)Only (ii) cannot be exactly representedc)Only (iii) and (iv) cannot be exactly representedd)Only (i) and (ii) cannot be exactly representedCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3⋅ b2b1b0where the position of the binary point is between b3and b2. Assume b7is the most significant bit. Some of the decimal numbers listed belowcannotbe representedexactlyin the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?a)None of (i), (ii), (iii), (iv) can be exactly representedb)Only (ii) cannot be exactly representedc)Only (iii) and (iv) cannot be exactly representedd)Only (i) and (ii) cannot be exactly representedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the unsigned 8-bit fixed point binary number representation, below, b7b6b5b4b3⋅ b2b1b0where the position of the binary point is between b3and b2. Assume b7is the most significant bit. Some of the decimal numbers listed belowcannotbe representedexactlyin the above representation: (i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001 Which one of the following statements is true?a)None of (i), (ii), (iii), (iv) can be exactly representedb)Only (ii) cannot be exactly representedc)Only (iii) and (iv) cannot be exactly representedd)Only (i) and (ii) cannot be exactly representedCorrect answer is option 'C'. Can you explain this answer?.
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