Number Systems Quiz

The binary representation of the decimal number 10 is 1010.

The binary and hexadecimal number systems are used in computers.

The hexadecimal equivalent of the decimal number 15 is F.

<p>The base of the octal number system is 8, using symbols <code>0</code> to <code>7</code>.</p> Signup and view all the answers

<p>The decimal number 25 is equivalent to <code>11001</code> in binary.</p> Signup and view all the answers

<p>The term 'base' refers to the number of unique digits, including zero, used to represent numbers in a system.</p> Signup and view all the answers

<p>The octal representation of the decimal number 8 is <code>10</code>.</p> Signup and view all the answers

<p>1110101</p> Signup and view all the answers

<p>10⁻³ or 0.001</p> Signup and view all the answers

<p>21</p> Signup and view all the answers

<p>64 and 64k</p> Signup and view all the answers

<p>101110</p> Signup and view all the answers

<p>Divide 125 by 2 repeatedly, tracking the remainders, to get 1111101 in binary.</p> Signup and view all the answers

<p>The binary representation is 0.1011.</p> Signup and view all the answers

<p>Multiply each bit by 2 raised to its weight and sum the results, yielding 43 in decimal.</p> Signup and view all the answers

<p>Multiply each digit by 8 raised to its weight and sum the totals to get 468 in decimal.</p> Signup and view all the answers

<p>Multiply each digit by 16 raised to its position's weight and sum all the results.</p> Signup and view all the answers

<p>Each remainder indicates a bit value in the binary representation, starting from the least significant bit.</p> Signup and view all the answers

<p>The value is 41 in decimal.</p> Signup and view all the answers

<p>The binary representation is 101001.1011.</p> Signup and view all the answers

<p>Multiply the fractional part by 2 and take the integer part iteratively until it reaches 0.</p> Signup and view all the answers

<p>Group the bits in threes starting from the right and convert each group to its octal equivalent.</p> Signup and view all the answers

<p>The octal equivalent is $1327_8$.</p> Signup and view all the answers

<p>Group the bits in fours starting from the right and convert each group to its hexadecimal representation.</p> Signup and view all the answers

<p>The hexadecimal equivalent is $2BB_{16}$.</p> Signup and view all the answers

<p>Use binary as an intermediary by first converting octal to binary, then binary to hexadecimal.</p> Signup and view all the answers

<p>The hexadecimal equivalent is $23E_{16}$.</p> Signup and view all the answers

<p>Grouping bits in threes aligns with the base-8 structure of the octal system.</p> Signup and view all the answers

<p>Binary serves as an intermediary format that allows for straightforward conversion between the two bases.</p> Signup and view all the answers

<p>Use binary as an intermediary by converting the hexadecimal digits to binary, then the resulting binary to octal.</p> Signup and view all the answers

<p>The octal equivalent is $17414_8$.</p> Signup and view all the answers

<p>The decimal equivalent of $1C3_{16}$ is $451_{10}$.</p> Signup and view all the answers

<p>The binary equivalent of $527_8$ is $101010111_2$.</p> Signup and view all the answers

<p>The octal representation of $2500_{10}$ is $4750_8$.</p> Signup and view all the answers

<p>The binary representation of $2B3_{16}$ is $001010110011_2$.</p> Signup and view all the answers

<p>The octal representation of $0.875_{10}$ is $0.7_8$.</p> Signup and view all the answers

<p>The decimal equivalent of $A5_{16}$ is $165_{10}$.</p> Signup and view all the answers

<p>The hexadecimal representation of $453_{10}$ is $1C5_{16}$.</p> Signup and view all the answers

<p>The binary form of $612_8$ is $110001010_2$.</p> Signup and view all the answers

<p>The octal representation of $0.625_{10}$ is $0.5_8$.</p> Signup and view all the answers