Q. If a number in base 5 is represented as '320', what is its decimal equivalent? (2023)
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Solution
The decimal equivalent of '320' in base 5 is calculated as (3 * 5^2) + (2 * 5^1) + (0 * 5^0) = 75 + 10 + 0 = 80.
Correct Answer:
B
— 80
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Q. If a number in base 5 is represented as 243, what is its decimal equivalent? (2023)
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Solution
The decimal equivalent of the base 5 number 243 is calculated as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 60.
Correct Answer:
A
— 60
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Q. If a number in base-6 is represented as 405, what is its decimal equivalent?
A.
145
B.
150
C.
155
D.
160
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Solution
To convert from base-6 to decimal, calculate 4*6^2 + 0*6^1 + 5*6^0 = 4*36 + 0 + 5 = 144 + 5 = 149.
Correct Answer:
B
— 150
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Q. If the base-2 number 1101 is converted to base-10, what is the result?
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Solution
To convert from base-2 to decimal, calculate 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13.
Correct Answer:
A
— 13
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Q. If the decimal number 10 is converted to binary, what is the resulting binary number? (2023)
A.
1010
B.
1001
C.
1100
D.
1110
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Solution
The decimal number 10 is represented as 1010 in binary.
Correct Answer:
A
— 1010
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Q. If the decimal number 15 is converted to binary, what is the resulting binary number?
A.
1110
B.
1111
C.
1101
D.
1011
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Solution
The decimal number 15 is represented as 1111 in binary.
Correct Answer:
B
— 1111
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Q. If the decimal number 255 is converted to binary, what is the resulting binary number?
A.
11111111
B.
11011111
C.
10111111
D.
10011111
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Solution
The decimal number 255 converts to binary as 11111111.
Correct Answer:
A
— 11111111
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Q. If the hexadecimal number A3 is converted to decimal, what is its value? (2023)
A.
163
B.
1630
C.
103
D.
83
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Solution
A3 in hexadecimal is calculated as 10*16^1 + 3*16^0 = 160 + 3 = 163.
Correct Answer:
A
— 163
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Q. If the number 1011 in binary is converted to decimal, what is its value?
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Solution
The binary number 1011 converts to decimal as follows: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.
Correct Answer:
A
— 11
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Q. In a base 3 system, what is the equivalent of the decimal number 5?
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Solution
The decimal number 5 is represented as 12 in base 3 (1*3^1 + 2*3^0 = 3 + 2 = 5).
Correct Answer:
B
— 21
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Q. In a base 3 system, what is the representation of the decimal number 5? (2023)
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Solution
In base 3, the decimal number 5 is represented as '12' (1*3^1 + 2*3^0 = 3 + 2 = 5).
Correct Answer:
B
— 21
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Q. In a base-3 numeral system, what is the representation of the decimal number 5? (2023)
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Solution
The decimal number 5 is represented as 21 in base-3 (2*3^1 + 1*3^0 = 5).
Correct Answer:
C
— 21
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Q. In a base-3 system, what is the sum of the base-3 numbers 12 and 21?
A.
110
B.
100
C.
102
D.
111
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Solution
To add in base-3, convert to decimal: 12 (base-3) = 3 + 2 = 5 (decimal) and 21 (base-3) = 2 + 0 = 2 (decimal). The sum is 5 + 2 = 7 (decimal), which is 21 in base-3.
Correct Answer:
A
— 110
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Q. In a base-4 system, what is the sum of the numbers '12' and '21'?
A.
33
B.
33 in base-4
C.
33 in base-10
D.
30 in base-4
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Solution
The sum of '12' and '21' in base-4 is '30' in base-4.
Correct Answer:
D
— 30 in base-4
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Q. In a base-4 system, what is the sum of the numbers 3 and 2?
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Solution
In base-4, the sum of 3 and 2 is 11 (3 + 2 = 5 in decimal, which is 11 in base-4).
Correct Answer:
A
— 11
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Q. In a base-5 number system, what is the decimal equivalent of the base-5 number 243?
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Solution
To convert from base-5 to decimal, multiply each digit by 5 raised to the power of its position (from right to left, starting at 0). Thus, 2*5^2 + 4*5^1 + 3*5^0 = 2*25 + 4*5 + 3*1 = 50 + 20 + 3 = 73.
Correct Answer:
A
— 35
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Q. In a base-5 numeral system, what is the decimal equivalent of the base-5 number 243? (2023)
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Solution
The base-5 number 243 is calculated as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 60 in decimal.
Correct Answer:
A
— 60
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Q. In a base-5 numeral system, what is the decimal equivalent of the number 243?
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Solution
The base-5 number 243 converts to decimal as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.
Correct Answer:
B
— 61
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Q. In a base-5 numeral system, what is the representation of the decimal number 10?
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Solution
In base-5, the decimal number 10 is represented as 20.
Correct Answer:
A
— 20
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Q. In a base-5 numeral system, what is the representation of the decimal number 12?
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Solution
In base-5, the decimal number 12 is represented as 22 (2*5^1 + 2*5^0 = 12).
Correct Answer:
B
— 23
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Q. In a base-5 numeral system, what is the representation of the decimal number 7?
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Solution
In base-5, the decimal number 7 is represented as 12, since 1*5^1 + 2*5^0 = 5 + 2 = 7.
Correct Answer:
A
— 12
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Q. In a base-5 numeral system, which of the following digits is not valid?
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Solution
In a base-5 numeral system, valid digits are 0, 1, 2, 3, and 4; thus, 5 is not valid.
Correct Answer:
D
— 5
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Q. In a base-7 system, what is the base-10 equivalent of the base-7 number 345?
A.
150
B.
170
C.
180
D.
190
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Solution
To convert from base-7 to decimal, calculate 3*7^2 + 4*7^1 + 5*7^0 = 3*49 + 4*7 + 5 = 147 + 28 + 5 = 180.
Correct Answer:
B
— 170
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Q. In a hexadecimal system, what is the decimal equivalent of the hexadecimal number 'A3'? (2023)
A.
163
B.
1630
C.
103
D.
83
Show solution
Solution
In hexadecimal, 'A' represents 10 and '3' represents 3. Therefore, A3 = (10 * 16^1) + (3 * 16^0) = 160 + 3 = 163.
Correct Answer:
A
— 163
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Q. In a numeral system, what does the term 'base' refer to? (2023)
A.
The number of unique digits used.
B.
The maximum value of a digit.
C.
The total number of digits in a number.
D.
The position of a digit in a number.
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Solution
The term 'base' refers to the number of unique digits used in a numeral system.
Correct Answer:
A
— The number of unique digits used.
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Q. In a numeral system, what does the term 'place value' refer to?
A.
The value of a digit based on its position.
B.
The total value of all digits combined.
C.
The maximum value a numeral can represent.
D.
The number of digits in a numeral.
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Solution
Place value refers to the value of a digit based on its position in a numeral.
Correct Answer:
A
— The value of a digit based on its position.
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Q. In converting the decimal number 255 to hexadecimal, what is the result?
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Solution
The decimal number 255 is represented as FF in hexadecimal.
Correct Answer:
A
— FF
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Q. In converting the hexadecimal number 'A3' to decimal, what is the resulting value?
A.
163
B.
1632
C.
123
D.
103
Show solution
Solution
The hexadecimal number 'A3' converts to decimal as follows: A (10)*16^1 + 3*16^0 = 160 + 3 = 163.
Correct Answer:
A
— 163
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Q. In converting the hexadecimal number 1A to decimal, what is the result?
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Solution
The hexadecimal number 1A converts to decimal as 1*16^1 + 10*16^0 = 26.
Correct Answer:
A
— 26
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Q. In the context of numeral systems, what does the term 'base' refer to?
A.
The number of unique digits used.
B.
The maximum value of a digit.
C.
The total number of digits in a system.
D.
The value of the first digit.
Show solution
Solution
The term 'base' refers to the number of unique digits used in a numeral system.
Correct Answer:
A
— The number of unique digits used.
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