Number System Quiz For Binary, Decimal, And Hexadecimal
Reviewed by Janaisa Harris
Janaisa Harris, BA (Mathematics)|
High School Math Teacher
Review Board Member
Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.
, BA (Mathematics)
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The "Number System Quiz for Binary, Decimal, and Hexadecimal" is an engaging exploration of fundamental numerical systems. In the world of mathematics and computer science, understanding binary, decimal, and hexadecimal numbering is essential. This quiz provides an opportunity to test and enhance your knowledge of these numbering systems. From converting numbers between binary, decimal, and hexadecimal formats to understanding their real-world applications, this quiz covers a wide range of topics.
Whether you're a math enthusiast, a computer science student, or simply curious about number systems, this quiz will challenge your skills and expand your understanding. Gain insights into the underlying Read moreprinciples of these numbering systems, explore how they're used in programming, and sharpen your problem-solving abilities. Whether you're a beginner looking to learn or an expert seeking a refresher, this quiz offers a stimulating experience for all.
Binary, Decimal, and Hexadecimal Questions and Answers
1.
What is the decimal equivalent of the binary number 11001?
A.
25
B.
13
C.
3
D.
28
Correct Answer
A. 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.
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2.
What is the binary equivalent of the decimal number 45?
A.
11100
B.
101101
C.
10100
D.
110110
Correct Answer
B. 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.
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3.
What is the binary equivalent of the hexadecimal number B2?
A.
100011
B.
11011
C.
11100011
D.
10110010
Correct Answer
D. 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.
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4.
What is the hexadecimal equivalent of the binary number 11011?
A.
1A
B.
B1
C.
1B
D.
2C
Correct Answer
C. 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.
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5.
What is the hexadecimal equivalent of the decimal number 20?
A.
14
B.
11
C.
19
D.
18
Correct Answer
A. 14
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.
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6.
What is the decimal equivalent of the hexadecimal number 2C?
A.
3A
B.
34
C.
44
D.
54
Correct Answer
C. 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.
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7.
What is the decimal equivalent of the binary number 10101100?
A.
162
B.
172
C.
182
D.
192
Correct Answer
B. 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.
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8.
What is the binary equivalent of the decimal number 168?
A.
10101110
B.
01000100
C.
10101000
D.
11101000
Correct Answer
C. 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.
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9.
What is the binary equivalent of the hexadecimal number 0x2301?
A.
0010001100000001
B.
1111110011111110
C.
1111000011001010
D.
0000001111110000
Correct Answer
A. 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.
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10.
What is the decimal equivalent of the binary number 11010010?
A.
75
B.
150
C.
210
D.
310
Correct Answer
C. 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.
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Janaisa Harris |BA (Mathematics)|
High School Math Teacher
Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a bachelor's degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher.
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