Convert the decimal number $13_{10}$ to base 2 (binary).
$111_2$
$1011_2$
$13_2$
$1101_2$
What is the decimal number $48_{10}$ represented in base 5?
$341_5$
$93_5$
$134_5$
$143_5$
The decimal number $75_{10}$ is equivalent to which number in base 8 (octal)?
$113_8$
$311_8$
$112_8$
$93_8$
Express the decimal number $25_{10}$ in base 3.
$221_3$
$212_3$
$81_3$
$122_3$
A basket contains $50_{10}$ apples. How would you write this number in base 6?
$82_6$
$221_6$
$122_6$
$132_6$
What is the decimal number $13$ converted to base 2 (binary)?
$1110_2$
$1001_2$
Convert the decimal number $28$ to base 5.
$301_5$
$103_5$
$53_5$
$130_5$
What is the representation of the decimal number $65$ in base 8 (octal)?
$11_8$
$110_8$
$101_8$
$81_8$
In the number $213_4$, what is the value of the digit '2' in our decimal system (base 10)?
$8$
$16$
$2$
$32$
Convert the decimal number $47$ into base 3.
$2102_3$
$1112_3$
$1202_3$
$2021_3$
What is the base-2 representation of the decimal number $29_{10}$?
$10111_2$
$11100_2$
$11011_2$
$11101_2$
Using the repeated division method, convert the decimal number $87_{10}$ to base-5.
$172_5$
$322_5$
$32_5$
$223_5$
What is the octal (base-8) equivalent of the decimal number $150_{10}$?
$622_8$
$228_8$
$226_8$
$186_8$
When converting the decimal number $45_{10}$ to base-3 using repeated division, what is the correct sequence of remainders obtained from the first division to the last?
1, 2, 0, 0
0, 0, 2, 1
1, 0, 2, 0
0, 0, 1, 2
In the repeated division method for converting a decimal number to another base, how are the remainders used to form the final number in the new base?
They are read from top to bottom.
They are added all together.
They are multiplied all together.
They are read from bottom to top.
When converting the decimal number $25_{10}$ to base 2, what is the first remainder you get after the first division?
$12$
$1$
$0$
What is the sequence of remainders obtained when converting the decimal number $48_{10}$ to base 5? The sequence should be written from the first remainder calculated to the last remainder calculated.
$1, 4, 3$
$5, 9, 1$
$3, 1, 4$
$3, 4, 1$
The remainders obtained when converting a decimal number to base 8 are, in order of calculation, $5$, then $3$. What is the number in base 8?
$58_8$
$53_8$
$35_8$
$85_8$
Using the method of division and remainders, convert the decimal number $130_{10}$ to base 6.
$334_6$
$433_6$
$214_6$
$343_6$
A student converted a decimal number to base 4. They performed the division process and got the remainders $3, 2, 1$ in that specific order of calculation. What was the original decimal number?
$27_{10}$
$321_{10}$
$123_{10}$
$45_{10}$
When converting a decimal number to another base (like base 2, 3, 5, etc.) using the repeated division method, the remainders are collected at each step. In what order should you read these remainders to form the final number in the new base?
By adding all the remainders together
In ascending order of the remainders' values
From the first remainder to the last (top to bottom)
From the last remainder to the first (bottom to top)
The number $29_{10}$ is converted to base 2. The steps of division are shown below:$29 \div 2 = 14$ Remainder $1$$14 \div 2 = 7$ Remainder $0$$7 \div 2 = 3$ Remainder $1$$3 \div 2 = 1$ Remainder $1$$1 \div 2 = 0$ Remainder $1$What is $29_{10}$ in base 2?
$10011_2$
A student converts the decimal number $47_{10}$ to base 5. They correctly find the remainders in this order: 2, 4, 1. However, they forget the rule about reading the remainders and write their answer as $241_5$. What is the correct answer?
$421_5$
$124_5$
$241_5$
$142_5$
Convert the decimal number $78_{10}$ to base 8 (octal). Remember to read the remainders in the correct order.
$96_8$
$611_8$
$116_8$
$161_8$
What is the decimal number $53_{10}$ when converted to base 3?
$2122_3$
$2212_3$
$1222_3$
$2221_3$
Convert the decimal number $63_{10}$ to its octal (base-8) equivalent.
$63_8$
$100_8$
$75_8$
$77_8$
What is the first step when converting the decimal number $45_{10}$ to octal (base-8) using the repeated division method?
Add $8$ to $45$.
Find the largest power of $8$ that is less than $45$.
Multiply $45$ by $8$.
Divide $45$ by $8$.
What is the octal representation of the decimal number $150_{10}$?
$230_8$
$176_8$
When converting a decimal number to octal, the remainders from the divisions by 8 form the octal number. In what order should you read these remainders?
In descending order of value.
From top to bottom (first remainder to last).
From bottom to top (last remainder to first).
In ascending order of value.
The octal number system uses digits from 0 to 7. Which of the following numbers cannot be an octal number?
$481_8$
$707_8$
$123_8$
$56_8$
What is the decimal number $10$ converted to Base-3?
$110_3$
$101_3$
$31_3$
$12_3$
What is the representation of the decimal number $25$ in Base-4?
$112_4$
$121_4$
$61_4$
$123_4$
The number $17$ in the decimal system is written as which number in the Base-3 system?
$102_3$
$52_3$
Convert the decimal number $39$ to its equivalent in Base-4.
$312_4$
$231_4$
$93_4$
$213_4$
A special counting system uses only the digits 0, 1, and 2. If you have 15 items, how would you write this quantity in this Base-3 system?
$120_3$
$210_3$
$112_3$
What is the decimal number $48$ converted to base-5?
$120_5$
Express the decimal number $75$ in base-6.
$300_6$
$203_6$
$302_6$
$213_6$
Which of the following is the base-5 representation of the decimal number $99$?
$344_5$
$334_5$
$443_5$
$243_5$
Convert the decimal number $115$ to base-6.
$131_6$
$113_6$
$251_6$
$311_6$
A box contains $64$ apples. How would you write this number in base-5?
$214_5$
$422_5$
$224_5$
$144_5$
Convert the decimal number $28.4$ to base 5. Which of the following is the correct representation?
$103.4_5$
$103.1_5$
$103.2_5$
$301.2_5$
A number in base 10 is $45$. What is this number in base 6?
$73_6$
$121_6$
How would you write the decimal number $15.5$ in base 8 (octal)?
$17.2_8$
$71.4_8$
$15.4_8$
$17.4_8$
What is the result of converting the decimal number $8.625$ to base 4?
$20.22_4$
$20.11_4$
$20.12_4$
$20.21_4$
The decimal number $13_{10}$ is converted to base 2 as $1101_2$. Which of the following expansions correctly verifies this conversion?
$1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0$
$1 + 1 + 0 + 1$
$1 \times 10^3 + 1 \times 10^2 + 0 \times 10^1 + 1 \times 10^0$
$1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1$
The expansion of a number in base 5 is given by the expression $2 \times 5^2 + 3 \times 5^1 + 4 \times 5^0$. What is its equivalent value in base 10?
$117_{10}$
$69_{10}$
$65_{10}$
$234_{10}$
A student converted the decimal number $45_{10}$ to base 6 and got $123_6$. Which statement is true when verifying this conversion by expanding $123_6$?
The conversion is incorrect because the expansion equals $48_{10}$.
The conversion is correct because the expansion equals $45_{10}$.
The conversion is incorrect because the expansion equals $51_{10}$.
The conversion is correct because the digits 1, 2, and 3 are all less than 6.
To verify if the conversion $100_{10} = 134_8$ is correct, a student writes the expansion: $1 \times 8^2 + 3 \times 8^1 + 4 \times 8^0$. What is the result of this expansion, and what does it indicate about the conversion?
The result is $88_{10}$, so the conversion is incorrect.
The result is $92_{10}$, so the conversion is incorrect.
The result is $100_{10}$, so the conversion is correct.
The result is $134_{10}$, so the conversion is incorrect.
The decimal number $37_{10}$ is equal to the base 4 number $2d1_4$, where d is a single digit. By setting up and solving an equation from the expansion of the base 4 number, find the value of d.
$d = 1$
$d = 3$
$d = 2$
$d = 0$
Convert the decimal number $10000$ to its binary (base-2) equivalent.
$10101010101010_2$
$10011100010000_2$
$11001100010000_2$
$10000100011100_2$
What is the binary representation of the decimal number $12345$?
$11000000111001_2$
$10011100000011_2$
$11000000111011_2$
$11000001110010_2$
The number $32768$ is a power of 2 (specifically $2^{15}$). What is its equivalent in the binary number system?
$111111111111111_2$
$1000000000000000_2$
$100000000000000_2$
$10000000000000000_2$
Which of the following binary numbers is equivalent to the decimal number $25000$?
$110000110101000_2$
$1000101011000011_2$
$11000011010100_2$
$11000110101000_2$
A computer program uses the number $65535$ to represent a maximum value. What is $65535$ in binary? (Hint: $65535 = 2^{16} - 1$)
$1010101010101010_2$
$1111111111111111_2$
Convert the decimal number $10000_{10}$ to its octal (base-8) equivalent.
$23420_8$
$24320_8$
$2342_8$
$20243_8$
What is the octal representation of the decimal number $12345_{10}$?
$17003_8$
$30171_8$
$3071_8$
$30071_8$
Convert the decimal number $65535_{10}$ to its base-8 equivalent.
$777771_8$
$177777_8$
$177776_8$
$77777_8$
Find the octal equivalent of the decimal number $45876_{10}$.
$113464_8$
$131464_8$
$464131_8$
$131564_8$
Which of the following is the correct base-8 representation of the decimal number $22222_{10}$?
$53316_8$
$53361_8$
$53136_8$
$61335_8$
Which of the following numbers, represented in different bases, has the largest value when converted to base 10?
$40000_5$
$12345_{10}$
$30100_8$
$2FFF_{16}$
A prize of 20000 dollars is awarded in a competition. What is the value of this prize represented in base 8 (octal)?
$24000_8$
$40470_8$
$47040_8$
$47004_8$
A number is written as $43210_5$ in base 5. What is its equivalent value in our standard base 10 system?
$194_{10}$
$4321_{10}$
$586_{10}$
$2930_{10}$
A legacy computer system from the 1970s uses octal (base-8) for its memory addressing. A critical data block is located at the decimal address $10000$. What is this address in octal?
$12500_8$
$02432_8$
$23421_8$
A data packet being sent over a computer network is assigned the sequence number $20000$. The underlying network protocol represents this number in binary (base-2). What is the binary representation of $20000$?
$100111000100000_2$
$100111000100001_2$
$101111000100000_2$
$100000100011100_2$
An explorer discovers a fictional alien civilization that uses a base-5 number system, perhaps because they have five fingers on one hand. The explorer counts the population of a major city to be $15625$ people. How would the aliens write this number?
$100000_5$
$15625_5$
$5000000_5$
$1000000_5$
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