Number System Trivia For Binary, Decimal, And Hexadecimal

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Quizzes Created: 16 | Total Attempts: 98,297
Questions: 10 | Viewed: 44,292

1.

Convert the binary number 11001 to decimal. The answer is:

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.

Convert the decimal number 45 to binary:

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.

Convert the hexadecimal number B2 to binary:

Explanation:
The hexadecimal number B2 can be converted to binary by replacing each digit of the hexadecimal number with its equivalent 4-bit binary representation. In this case, B is equivalent to 1011 and 2 is equivalent to 0010. Combining these binary representations gives the binary number 10110010.
4.

Convert the binary number 11011 to hexadecimal:

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.
5.

Convert the decimal number 20 to hexadecimal:

Explanation:
The decimal number 20 can be converted to hexadecimal by dividing it by 16 repeatedly and noting down the remainders. The remainders in this case are 4 and 1, which correspond to the hexadecimal digits 4 and 1. Therefore, the hexadecimal representation of the decimal number 20 is 14.
6.

Convert the hexadecimal number 2C to decimal:

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.
7.

Convert the binary number 10101100 to its decimal equivalent:

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.
8.

Convert the decimal number 168 to binary equivalent:

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.

Convert the hexadecimal number 0x2301 to its binary equivalent:

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.
10.