GATE Exam > GATE Questions > Convert the 127 decimal number into binary.a)...
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Convert the 127 decimal number into binary.
- a)1100111
- b)1111111
- c)1111011
- d)111111
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Convert the 127 decimal number into binary.a)1100111b)1111111c)1111011...
Converting 127 decimal number into binary:
Step 1: Divide the decimal number by 2 and note down the quotient and remainder.
Step 2: Continue dividing the quotient by 2 until the quotient becomes 0.
Step 3: Write the remainders in reverse order to get the binary equivalent.
Using this method, we can convert the given decimal numbers into binary as follows:
Option A: 1100111
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Binary equivalent = 1111111 (incorrect)
Option B: 1111111
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Binary equivalent = 1111111 (correct)
Option C: 1111011
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Binary equivalent = 1111111 (incorrect)
Option D: 111111
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- Binary equivalent = 1111111 (incorrect)
Therefore, the correct answer is option B (1111111).
Step 1: Divide the decimal number by 2 and note down the quotient and remainder.
Step 2: Continue dividing the quotient by 2 until the quotient becomes 0.
Step 3: Write the remainders in reverse order to get the binary equivalent.
Using this method, we can convert the given decimal numbers into binary as follows:
Option A: 1100111
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Binary equivalent = 1111111 (incorrect)
Option B: 1111111
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Binary equivalent = 1111111 (correct)
Option C: 1111011
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- 1 ÷ 2 = 0 remainder 1
- Binary equivalent = 1111111 (incorrect)
Option D: 111111
- 127 ÷ 2 = 63 remainder 1
- 63 ÷ 2 = 31 remainder 1
- 31 ÷ 2 = 15 remainder 1
- 15 ÷ 2 = 7 remainder 1
- 7 ÷ 2 = 3 remainder 1
- 3 ÷ 2 = 1 remainder 1
- Binary equivalent = 1111111 (incorrect)
Therefore, the correct answer is option B (1111111).
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Community Answer
Convert the 127 decimal number into binary.a)1100111b)1111111c)1111011...
Concept
Divide 127 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.
Write the remainder from bottom to top i.e. in the reverse chronological order.
This will give the binary equivalent of 127.
Therefore, the binary equivalent of decimal number 127 is 1111111.
Divide 127 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.
Write the remainder from bottom to top i.e. in the reverse chronological order.
This will give the binary equivalent of 127.
Therefore, the binary equivalent of decimal number 127 is 1111111.
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Convert the 127 decimal number into binary.a)1100111b)1111111c)1111011d)111111Correct answer is option 'B'. Can you explain this answer?
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