Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a 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. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
, BA-Mathematics
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Do you know how to count in binary? Take this Binary quiz and test your knowledge. If you are starting your lessons on programming, one of the things that you need to understand is binary code. By doing this, you are well on your way to understanding the different programming theories and languages. How good are you at converting decimal numbers to binary? Test your binary skills in the binary test below, and remember that each answer is used only once. All the best, and keep practicing!
Binary Counting Questions and Answers
1.
Convert 30 into a binary number.
A.
00011110
B.
00001001
C.
00101000
D.
00010010
E.
00110111
Correct Answer A. 00011110
Explanation The correct answer is: 00011110To convert the decimal number 30 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 30 by 2:30 Ã· 2 = 15 remainder 0(Least significant bit: 0)Divide 15 by 2:15 Ã· 2 = 7 remainder 1(Next bit: 1)Divide 7 by 2:7 Ã· 2 = 3 remainder 1(Next bit: 1)Divide 3 by 2:3 Ã· 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00011110So, the binary representation of 30 is 00011110.
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2.
Convert 40 into a binary number.
A.
00011110
B.
00001001
C.
00101000
D.
00010010
E.
00110111
Correct Answer C. 00101000
Explanation The correct answer is: 00101000To convert the decimal number 40 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 40 by 2:40 Ã· 2 = 20 remainder 0(Least significant bit: 0)Divide 20 by 2:20 Ã· 2 = 10 remainder 0(Next bit: 0)Divide 10 by 2:10 Ã· 2 = 5 remainder 0(Next bit: 0)Divide 5 by 2:5 Ã· 2 = 2 remainder 1(Next bit: 1)Divide 2 by 2:2 Ã· 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00101000So, the binary representation of 40 is 00101000.
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3.
Convert 55 into a binary number.
A.
00011110
B.
00001001
C.
00101000
D.
00010010
E.
00110111
Correct Answer E. 00110111
Explanation The correct answer is: 00110111To convert the decimal number 55 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 55 by 2:55 Ã· 2 = 27 remainder 1(Least significant bit: 1)Divide 27 by 2:27 Ã· 2 = 13 remainder 1(Next bit: 1)Divide 13 by 2:13 Ã· 2 = 6 remainder 1(Next bit: 1)Divide 6 by 2:6 Ã· 2 = 3 remainder 0(Next bit: 0)Divide 3 by 2:3 Ã· 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00110111So, the binary representation of 55 is 00110111.
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4.
Convert 63 into a binary number.
A.
00111111
B.
10000000
C.
01101001
D.
01001110
E.
01011010
Correct Answer A. 00111111
Explanation To convert the decimal number 63 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 63 by 2:63 Ã· 2 = 31 remainder 1(Least significant bit: 1)Divide 31 by 2:31 Ã· 2 = 15 remainder 1(Next bit: 1)Divide 15 by 2:15 Ã· 2 = 7 remainder 1(Next bit: 1)Divide 7 by 2:7 Ã· 2 = 3 remainder 1(Next bit: 1)Divide 3 by 2:3 Ã· 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 00111111So, the binary representation of 63 is 00111111.
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5.
Convert 78 into a binary number.
A.
00111111
B.
10000000
C.
01101001
D.
01001110
E.
01011010
Correct Answer D. 01001110
Explanation The correct answer is: 01001110To convert the decimal number 78 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 78 by 2:78 Ã· 2 = 39 remainder 0(Least significant bit: 0)Divide 39 by 2:39 Ã· 2 = 19 remainder 1(Next bit: 1)Divide 19 by 2:19 Ã· 2 = 9 remainder 1(Next bit: 1)Divide 9 by 2:9 Ã· 2 = 4 remainder 1(Next bit: 1)Divide 4 by 2:4 Ã· 2 = 2 remainder 0(Next bit: 0)Divide 2 by 2:2 Ã· 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 01001110So, the binary representation of 78 is 01001110.
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6.
Convert 90 into a binary number.
A.
00111111
B.
10000000
C.
01101001
D.
01001110
E.
1011010
Correct Answer E. 1011010
Explanation The correct binary representation of 90 is 1011010.To convert the decimal number 90 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 90 by 2:90 Ã· 2 = 45 remainder 0(Least significant bit: 0)Divide 45 by 2:45 Ã· 2 = 22 remainder 1(Next bit: 1)Divide 22 by 2:22 Ã· 2 = 11 remainder 0(Next bit: 0)Divide 11 by 2:11 Ã· 2 = 5 remainder 1(Next bit: 1)Divide 5 by 2:5 Ã· 2 = 2 remainder 1(Next bit: 1)Divide 2 by 2:2 Ã· 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 1011010So, the binary representation of 90 is 1011010.
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7.
Convert 105 into a binary number.
A.
00111111
B.
10000000
C.
01101001
D.
01001110
E.
01011010
Correct Answer C. 01101001
Explanation The correct answer is: 01101001To convert the decimal number 105 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 105 by 2:105 Ã· 2 = 52 remainder 1(Least significant bit: 1)Divide 52 by 2:52 Ã· 2 = 26 remainder 0(Next bit: 0)Divide 26 by 2:26 Ã· 2 = 13 remainder 0(Next bit: 0)Divide 13 by 2:13 Ã· 2 = 6 remainder 1(Next bit: 1)Divide 6 by 2:6 Ã· 2 = 3 remainder 0(Next bit: 0)Divide 3 by 2:3 Ã· 2 = 1 remainder 1(Next bit: 1)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 01101001So, the binary representation of 105 is 01101001.
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8.
Convert 128 into a binary number.
A.
00111111
B.
10000000
C.
01101001
D.
01001110
E.
01011010
Correct Answer B. 10000000
Explanation The correct answer is: 10000000To convert the decimal number 128 into binary, you can use repeated division by 2 and keep track of the remainders. However, in this case, it is important to note that 128 is a power of 2 (2^7), so its binary representation will have only one '1' followed by seven '0's.So, the binary representation of 128 is 10000000.
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9.
Convert 156 into a binary number.
A.
10000110
B.
10011100
C.
10011111
D.
11100111
Correct Answer B. 10011100
Explanation The correct answer is: 10011100To convert the decimal number 156 into binary, you can use repeated division by 2 and keep track of the remainders. Here's the step-by-step process:Divide 156 by 2:156 Ã· 2 = 78 remainder 0(Least significant bit: 0)Divide 78 by 2:78 Ã· 2 = 39 remainder 0(Next bit: 0)Divide 39 by 2:39 Ã· 2 = 19 remainder 1(Next bit: 1)Divide 19 by 2:19 Ã· 2 = 9 remainder 1(Next bit: 1)Divide 9 by 2:9 Ã· 2 = 4 remainder 1(Next bit: 1)Divide 4 by 2:4 Ã· 2 = 2 remainder 0(Next bit: 0)Divide 2 by 2:2 Ã· 2 = 1 remainder 0(Next bit: 0)Divide 1 by 2:1 Ã· 2 = 0 remainder 1(Most significant bit: 1)Now, combine the remainders in reverse order: 10011100So, the binary representation of 156 is 10011100.
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10.
Convert 199 into a binary number.
A.
11110000
B.
11001100
C.
11000111
D.
10101010
Correct Answer C. 11000111
Explanation To convert a decimal number into a binary number, we divide the decimal number by 2 repeatedly and record the remainders. Starting with 199, we divide it by 2 to get a quotient of 99 and a remainder of 1. We then divide 99 by 2 to get a quotient of 49 and a remainder of 1. Continuing this process, we divide 49 by 2 to get a quotient of 24 and a remainder of 1. We divide 24 by 2 to get a quotient of 12 and a remainder of 0. We divide 12 by 2 to get a quotient of 6 and a remainder of 0. We divide 6 by 2 to get a quotient of 3 and a remainder of 0. Finally, we divide 3 by 2 to get a quotient of 1 and a remainder of 1. The binary representation of 199 is therefore 11000111.
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Janaisa Harris |BA-Mathematics|
Mathematics Expert
Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a 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. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
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