Number System Quiz For Binary, Decimal, And Hexadecimal

1. What is the decimal equivalent of the binary number 11001?

25

13

3

28

To convert a binary number to decimal, each digit in the binary number is multiplied by 2 raised to the power of its position, starting from the rightmost digit. In this case, the binary number 11001 has five digits. Starting from the rightmost digit, the first digit is 1, so it is multiplied by 2 raised to the power of 0 (2^0 = 1). The second digit is 0, so it is multiplied by 2 raised to the power of 1 (2^1 = 2). The third digit is also 0, so it is multiplied by 2 raised to the power of 2 (2^2 = 4). The fourth digit is 1, so it is multiplied by 2 raised to the power of 3 (2^3 = 8). The fifth digit is 1, so it is multiplied by 2 raised to the power of 4 (2^4 = 16). Adding all these results together, 1 + 0 + 0 + 8 + 16 = 25.

Explanation

To convert a binary number to decimal, each digit in the binary number is multiplied by 2 raised to the power of its position, starting from the rightmost digit. In this case, the binary number 11001 has five digits. Starting from the rightmost digit, the first digit is 1, so it is multiplied by 2 raised to the power of 0 (2^0 = 1). The second digit is 0, so it is multiplied by 2 raised to the power of 1 (2^1 = 2). The third digit is also 0, so it is multiplied by 2 raised to the power of 2 (2^2 = 4). The fourth digit is 1, so it is multiplied by 2 raised to the power of 3 (2^3 = 8). The fifth digit is 1, so it is multiplied by 2 raised to the power of 4 (2^4 = 16). Adding all these results together, 1 + 0 + 0 + 8 + 16 = 25.

2. What is the binary equivalent of the decimal number 45?

11100

101101

10100

110110

The given decimal number 45 is converted to binary as 101101. You will keep dividing by 2 until you get to 0. If you have a reminder that will represent 1, if you do not have a remainder it will represent 0. We will start by dividing 45 by 2 then continue until we get to 0. 45/2 = 22 with a remainder (1). 22/2 = 11 with no remainder (0). 11/2 = 5 with a remainder (1). 5/2 = 2 with a remainder (1). 2/2 = 1 with no remainder (0) . 1/2 = 0 with a remainder (1). Thus, if we put in order the numbers with a remainder and not a remainder it will be 101101.

Explanation

The given decimal number 45 is converted to binary as 101101. You will keep dividing by 2 until you get to 0. If you have a reminder that will represent 1, if you do not have a remainder it will represent 0. We will start by dividing 45 by 2 then continue until we get to 0. 45/2 = 22 with a remainder (1). 22/2 = 11 with no remainder (0). 11/2 = 5 with a remainder (1). 5/2 = 2 with a remainder (1). 2/2 = 1 with no remainder (0) . 1/2 = 0 with a remainder (1). Thus, if we put in order the numbers with a remainder and not a remainder it will be 101101.

3. What is the decimal equivalent of the binary number 111101?

55

61

47

45

To convert the binary number 111101 to decimal, each digit is multiplied by 2 raised to its positional power from right to left. The calculation is: (1×2⁵) + (1×2⁴) + (1×2³) + (1×2²) + (0×2¹) + (1×2⁰). This results in 32 + 16 + 8 + 4 + 0 + 1 = 61. Since the correct decimal equivalent of 111101 is 61, the answer is option B. Binary numbers are always converted using base-2, where each digit represents a power of 2. By summing up these values, we can accurately determine the decimal representation of a given binary number.

Explanation

To convert the binary number 111101 to decimal, each digit is multiplied by 2 raised to its positional power from right to left. The calculation is: (1×2⁵) + (1×2⁴) + (1×2³) + (1×2²) + (0×2¹) + (1×2⁰). This results in 32 + 16 + 8 + 4 + 0 + 1 = 61. Since the correct decimal equivalent of 111101 is 61, the answer is option B. Binary numbers are always converted using base-2, where each digit represents a power of 2. By summing up these values, we can accurately determine the decimal representation of a given binary number.

4. What is the decimal equivalent of the binary number 10101100?

162

172

182

192

To convert a binary number to its decimal equivalent, each digit in the binary number is multiplied by the corresponding power of 2 and then summed up. In this case, the binary number 10101100 can be broken down as follows: (1 * 2^7) + (0 * 2^6) + (1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = 128 + 0 + 32 + 0 + 8 + 4 + 0 + 0 = 172. Therefore, the decimal equivalent of the binary number 10101100 is 172.

Explanation

To convert a binary number to its decimal equivalent, each digit in the binary number is multiplied by the corresponding power of 2 and then summed up. In this case, the binary number 10101100 can be broken down as follows: (1 * 2^7) + (0 * 2^6) + (1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = 128 + 0 + 32 + 0 + 8 + 4 + 0 + 0 = 172. Therefore, the decimal equivalent of the binary number 10101100 is 172.

5. What is the decimal equivalent of the binary number 11010010?

75

150

210

310

To convert a binary number to a decimal number, we need to multiply each digit of the binary number by the corresponding power of 2 and sum them up. In this case, starting from the rightmost digit, we have 0 multiplied by 2^0 (which is 0), 1 multiplied by 2^1 (which is 2), 0 multiplied by 2^2 (which is 0), 0 multiplied by 2^3 (which is 0), 1 multiplied by 2^4 (which is 16), 0 multiplied by 2^5 (which is 0), 1 multiplied by 2^6 (which is 64), and 1 multiplied by 2^7 (which is 128). Summing them up, we get 2 + 16 + 64 + 128 = 210. Therefore, the correct answer is 210.

Explanation

To convert a binary number to a decimal number, we need to multiply each digit of the binary number by the corresponding power of 2 and sum them up. In this case, starting from the rightmost digit, we have 0 multiplied by 2^0 (which is 0), 1 multiplied by 2^1 (which is 2), 0 multiplied by 2^2 (which is 0), 0 multiplied by 2^3 (which is 0), 1 multiplied by 2^4 (which is 16), 0 multiplied by 2^5 (which is 0), 1 multiplied by 2^6 (which is 64), and 1 multiplied by 2^7 (which is 128). Summing them up, we get 2 + 16 + 64 + 128 = 210. Therefore, the correct answer is 210.

6. What is the binary equivalent of the hexadecimal number B2?

100011

11011

11100011

10110010

To convert a hexadecimal number to its binary equivalent, each hexadecimal digit is represented by its corresponding 4-bit binary value. Let's break it down for the hexadecimal number B2:

The hexadecimal digit B corresponds to 11 in decimal, and its binary equivalent is 1011.

The hexadecimal digit 2 corresponds to 2 in decimal, and its binary equivalent is 0010.

Therefore, the binary equivalent of the hexadecimal number B2 is the combination of these two parts: B (1011) and 2 (0010), which gives us 10110010.

Thus, the correct binary equivalent of B2 is 10110010.

Explanation

To convert a hexadecimal number to its binary equivalent, each hexadecimal digit is represented by its corresponding 4-bit binary value. Let's break it down for the hexadecimal number B2:

The hexadecimal digit B corresponds to 11 in decimal, and its binary equivalent is 1011.

The hexadecimal digit 2 corresponds to 2 in decimal, and its binary equivalent is 0010.

Therefore, the binary equivalent of the hexadecimal number B2 is the combination of these two parts: B (1011) and 2 (0010), which gives us 10110010.

Thus, the correct binary equivalent of B2 is 10110010.

7. Which binary number represents the decimal number 29?

11011

10101

11101

10011

To convert the decimal number 29 into binary, we divide by 2 repeatedly and record the remainders. 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. Reading the remainders from bottom to top, the binary equivalent of 29 is 11101. Comparing this with the given options, option C is correct. This method of successive division by 2 is the standard way of converting any decimal number to its binary representation.

Explanation

To convert the decimal number 29 into binary, we divide by 2 repeatedly and record the remainders. 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. Reading the remainders from bottom to top, the binary equivalent of 29 is 11101. Comparing this with the given options, option C is correct. This method of successive division by 2 is the standard way of converting any decimal number to its binary representation.

8. What is the binary equivalent of the decimal number 168?

10101110

01000100

10101000

11101000

The correct answer is 10101000 because when converting the decimal number 168 to binary, we divide the number by 2 and record the remainder until the quotient becomes 0. The remainders in reverse order give us the binary equivalent. In this case, when dividing 168 by 2, we get a remainder of 0. Dividing the resulting quotient (84) by 2 gives a remainder of 0 again. Continuing this process, we get remainders of 1, 0, 1, 0, and 1 respectively. Therefore, the binary equivalent of 168 is 10101000.

Explanation

The correct answer is 10101000 because when converting the decimal number 168 to binary, we divide the number by 2 and record the remainder until the quotient becomes 0. The remainders in reverse order give us the binary equivalent. In this case, when dividing 168 by 2, we get a remainder of 0. Dividing the resulting quotient (84) by 2 gives a remainder of 0 again. Continuing this process, we get remainders of 1, 0, 1, 0, and 1 respectively. Therefore, the binary equivalent of 168 is 10101000.

9. What is the hexadecimal equivalent of the decimal number 20?

14

11

19

18

To convert the decimal number 20 to hexadecimal, divide it by 16. Since 20 ÷ 16 = 1 remainder 4, the quotient (1) becomes the leftmost digit, and the remainder (4) is the rightmost digit. This means 20 in hexadecimal is written as 14. Checking the given options—14, 11, 19, and 18—the correct answer is 14, which matches option A. The conversion follows the standard division method, where the quotient gives the most significant digit, and the remainder provides the least significant digit, ensuring accurate hexadecimal representation of the decimal number.

Explanation

To convert the decimal number 20 to hexadecimal, divide it by 16. Since 20 ÷ 16 = 1 remainder 4, the quotient (1) becomes the leftmost digit, and the remainder (4) is the rightmost digit. This means 20 in hexadecimal is written as 14. Checking the given options—14, 11, 19, and 18—the correct answer is 14, which matches option A. The conversion follows the standard division method, where the quotient gives the most significant digit, and the remainder provides the least significant digit, ensuring accurate hexadecimal representation of the decimal number.

10. What is the decimal equivalent of the hexadecimal number 2C?

3A

34

44

54

To convert a hexadecimal number to decimal, each digit in the hexadecimal number is multiplied by the corresponding power of 16 and then summed. In this case, the hexadecimal number is 2C. The first digit 2 is multiplied by 16^1 (16) and the second digit C is multiplied by 16^0 (1), resulting in 32 + 12 = 44 in decimal. Therefore, the correct answer is 44.

Explanation

To convert a hexadecimal number to decimal, each digit in the hexadecimal number is multiplied by the corresponding power of 16 and then summed. In this case, the hexadecimal number is 2C. The first digit 2 is multiplied by 16^1 (16) and the second digit C is multiplied by 16^0 (1), resulting in 32 + 12 = 44 in decimal. Therefore, the correct answer is 44.

11. How many bits are needed to represent the decimal number 200 in binary?

6

7

8

9

The number of bits required to represent a decimal number in binary depends on how many powers of 2 are needed. The largest power of 2 less than or equal to 200 is 2⁷ = 128. We continue: 200 - 128 = 72, 72 - 64 (2⁶) = 8, 8 - 8 (2³) = 0. The binary representation of 200 is 11001000, which consists of 8 bits. The correct answer is option C, 8. The number of bits is determined by finding the highest power of 2 and counting all required binary digits.

Explanation

The number of bits required to represent a decimal number in binary depends on how many powers of 2 are needed. The largest power of 2 less than or equal to 200 is 2⁷ = 128. We continue: 200 - 128 = 72, 72 - 64 (2⁶) = 8, 8 - 8 (2³) = 0. The binary representation of 200 is 11001000, which consists of 8 bits. The correct answer is option C, 8. The number of bits is determined by finding the highest power of 2 and counting all required binary digits.

12. What is the decimal value of the hexadecimal number 3F?

48

57

63

72

To convert the hexadecimal number 3F to decimal, multiply each digit by its corresponding power of 16. 3 is in the 16¹ place, and F (which is 15 in decimal) is in the 16⁰ place. The calculation is (3×16¹) + (15×16⁰) = (3×16) + (15×1) = 48 + 15 = 63. Comparing this with the given options, 63 is the correct decimal value of 3F, making option C correct. The conversion process follows the place value system where each digit is multiplied by increasing powers of 16 from right to left.

Explanation

To convert the hexadecimal number 3F to decimal, multiply each digit by its corresponding power of 16. 3 is in the 16¹ place, and F (which is 15 in decimal) is in the 16⁰ place. The calculation is (3×16¹) + (15×16⁰) = (3×16) + (15×1) = 48 + 15 = 63. Comparing this with the given options, 63 is the correct decimal value of 3F, making option C correct. The conversion process follows the place value system where each digit is multiplied by increasing powers of 16 from right to left.

13. What is the hexadecimal equivalent of the binary number 11011?

1A

B1

1B

2C

To convert a binary number to hexadecimal, we group the binary digits into sets of four starting from the rightmost digit. In this case, we have 1101 and 1. We then convert each group of four binary digits to their corresponding hexadecimal digit. 1101 is equivalent to D in hexadecimal, and 1 is equivalent to 1 in hexadecimal. Therefore, combining these two hexadecimal digits, we get the hexadecimal representation of the binary number 11011 as 1B.

Explanation

To convert a binary number to hexadecimal, we group the binary digits into sets of four starting from the rightmost digit. In this case, we have 1101 and 1. We then convert each group of four binary digits to their corresponding hexadecimal digit. 1101 is equivalent to D in hexadecimal, and 1 is equivalent to 1 in hexadecimal. Therefore, combining these two hexadecimal digits, we get the hexadecimal representation of the binary number 11011 as 1B.

14. What is the binary equivalent of the hexadecimal number 0x2301?

0010001100000001

1111110011111110

1111000011001010

0000001111110000

To convert a hexadecimal number to its binary equivalent, you can use the following steps:

Write down the hexadecimal number: 0x2301

Convert each hexadecimal digit to its 4-bit binary representation:

2 (hex) = 0010 (binary)

3 (hex) = 0011 (binary)

0 (hex) = 0000 (binary)

1 (hex) = 0001 (binary)

Combine the binary representations of each digit:

0010 0011 0000 0001

So, the binary equivalent of the hexadecimal number 0x2301 is 0010001100000001.

Explanation

To convert a hexadecimal number to its binary equivalent, you can use the following steps:

Write down the hexadecimal number: 0x2301

Convert each hexadecimal digit to its 4-bit binary representation:

2 (hex) = 0010 (binary)

3 (hex) = 0011 (binary)

0 (hex) = 0000 (binary)

1 (hex) = 0001 (binary)

Combine the binary representations of each digit:

0010 0011 0000 0001

So, the binary equivalent of the hexadecimal number 0x2301 is 0010001100000001.

15. What is the hexadecimal equivalent of the decimal number 92?

5C

6A

4F

7C

To convert decimal 92 to hexadecimal, divide the number by 16 (since hexadecimal is base 16). Dividing 92 by 16 gives a quotient of 5 and a remainder of 12. In hexadecimal, 5 remains 5, and 12 corresponds to the letter C (as hexadecimal uses A–F for values 10–15). Combining the two parts, the result is 5C. This two-digit hexadecimal representation accurately reflects the base-16 value of decimal 92. Therefore, 92 in decimal equals 5C in hexadecimal.

Explanation

To convert decimal 92 to hexadecimal, divide the number by 16 (since hexadecimal is base 16). Dividing 92 by 16 gives a quotient of 5 and a remainder of 12. In hexadecimal, 5 remains 5, and 12 corresponds to the letter C (as hexadecimal uses A–F for values 10–15). Combining the two parts, the result is 5C. This two-digit hexadecimal representation accurately reflects the base-16 value of decimal 92. Therefore, 92 in decimal equals 5C in hexadecimal.