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If the number 235 in decimal system is converted into binary system, then what is the resulting number ?
- a)(111 10011)2
- b)(11101011)2
- c)(11110101)2
- d)(11011011)2
Correct answer is option 'B'. Can you explain this answer?
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Understanding Decimal to Binary Conversion
Converting the decimal number 235 to binary involves dividing the number by 2 and recording the remainders. The process continues until the quotient becomes zero. The binary representation is then formed by reading the remainders in reverse order.
Step-by-Step Conversion
1. **Divide and Record Remainders:**
- 235 ÷ 2 = 117, remainder = 1
- 117 ÷ 2 = 58, remainder = 1
- 58 ÷ 2 = 29, remainder = 0
- 29 ÷ 2 = 14, remainder = 1
- 14 ÷ 2 = 7, remainder = 0
- 7 ÷ 2 = 3, remainder = 1
- 3 ÷ 2 = 1, remainder = 1
- 1 ÷ 2 = 0, remainder = 1
2. **Collect the Remainders:**
- The remainders collected in reverse order are: 1, 1, 1, 1, 0, 1, 0, 1.
3. **Final Binary Representation:**
- Therefore, the binary equivalent of 235 is **11101011**.
Correct Answer
- The correct option is **(b) (11101011)₂**.
Verification
To verify, we can convert **11101011** back to decimal:
- \(1 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
- \(= 128 + 64 + 32 + 0 + 8 + 0 + 2 + 1\)
- \(= 235\)
This confirms that the conversion is accurate.
Conclusion
Thus, when 235 is converted into binary, the correct binary representation is indeed **(11101011)₂**.
Converting the decimal number 235 to binary involves dividing the number by 2 and recording the remainders. The process continues until the quotient becomes zero. The binary representation is then formed by reading the remainders in reverse order.
Step-by-Step Conversion
1. **Divide and Record Remainders:**
- 235 ÷ 2 = 117, remainder = 1
- 117 ÷ 2 = 58, remainder = 1
- 58 ÷ 2 = 29, remainder = 0
- 29 ÷ 2 = 14, remainder = 1
- 14 ÷ 2 = 7, remainder = 0
- 7 ÷ 2 = 3, remainder = 1
- 3 ÷ 2 = 1, remainder = 1
- 1 ÷ 2 = 0, remainder = 1
2. **Collect the Remainders:**
- The remainders collected in reverse order are: 1, 1, 1, 1, 0, 1, 0, 1.
3. **Final Binary Representation:**
- Therefore, the binary equivalent of 235 is **11101011**.
Correct Answer
- The correct option is **(b) (11101011)₂**.
Verification
To verify, we can convert **11101011** back to decimal:
- \(1 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
- \(= 128 + 64 + 32 + 0 + 8 + 0 + 2 + 1\)
- \(= 235\)
This confirms that the conversion is accurate.
Conclusion
Thus, when 235 is converted into binary, the correct binary representation is indeed **(11101011)₂**.
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If the number 235 in decimal system is converted into binary system, then what is the resulting number ?a)(111 10011)2b)(11101011)2c)(11110101)2d)(11011011)2Correct answer is option 'B'. Can you explain this answer?
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