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Which of the following is the decimal and hexadecimal equivalents of the binary number 10011101?
- a)155, 0x9B
- b)157, 0x9D
- c)159, 0x9F
- d)185, 0xB9
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Which of the following is the decimal and hexadecimal equivalents of t...
To turn a binary number into decimal, you just have to add the values of each bit that is a 1. The values of 10011101 are 128, 16, 8, 4, and 1. 128 + 16 + 8 + 4 + 1 = 157.
Hexadecimal is a base-16 number system. The values of hexadecimal are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F-16 characters total, from which to create all the numbers you'll ever need. So, if 1001 in binary is 9, then the hexadecimal equivalent is 9. Since we then have 1101, which is 13 in binary, the hexadecimal answer is D and the complete hexadecimal answer is 0x9D.
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Which of the following is the decimal and hexadecimal equivalents of t...
Understanding Binary to Decimal Conversion
To convert the binary number 10011101 to decimal, we evaluate each bit's value based on its position.
- Each binary digit (bit) has a value of 2 raised to its position index, starting from 0 on the right.
- The binary number 10011101 can be broken down as follows:
- 1 × 2^7 = 128
- 0 × 2^6 = 0
- 0 × 2^5 = 0
- 1 × 2^4 = 16
- 1 × 2^3 = 8
- 1 × 2^2 = 4
- 0 × 2^1 = 0
- 1 × 2^0 = 1
- Adding these values together: 128 + 0 + 0 + 16 + 8 + 4 + 0 + 1 = 157
Converting Decimal to Hexadecimal
Once we have the decimal equivalent (157), we can convert it to hexadecimal.
- To convert decimal to hexadecimal, divide the decimal number by 16 and note the remainder:
- 157 ÷ 16 = 9 remainder 13 (D in hexadecimal)
- Reading from top to bottom gives us 9D.
Final Results
Thus, the binary number 10011101 has the following equivalents:
- Decimal: 157
- Hexadecimal: 0x9D
Therefore, the correct answer is option 'B': 157, 0x9D.
To convert the binary number 10011101 to decimal, we evaluate each bit's value based on its position.
- Each binary digit (bit) has a value of 2 raised to its position index, starting from 0 on the right.
- The binary number 10011101 can be broken down as follows:
- 1 × 2^7 = 128
- 0 × 2^6 = 0
- 0 × 2^5 = 0
- 1 × 2^4 = 16
- 1 × 2^3 = 8
- 1 × 2^2 = 4
- 0 × 2^1 = 0
- 1 × 2^0 = 1
- Adding these values together: 128 + 0 + 0 + 16 + 8 + 4 + 0 + 1 = 157
Converting Decimal to Hexadecimal
Once we have the decimal equivalent (157), we can convert it to hexadecimal.
- To convert decimal to hexadecimal, divide the decimal number by 16 and note the remainder:
- 157 ÷ 16 = 9 remainder 13 (D in hexadecimal)
- Reading from top to bottom gives us 9D.
Final Results
Thus, the binary number 10011101 has the following equivalents:
- Decimal: 157
- Hexadecimal: 0x9D
Therefore, the correct answer is option 'B': 157, 0x9D.
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