Number Systems and Conversion Techniques

The symbols used in the hexadecimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

Binary and hexadecimal number systems are used by computers, while the decimal system is used by humans.

The binary equivalent of the decimal number 10 is 1010.

<p>The base of the octal number system is 8, and it uses the symbols 0, 1, 2, 3, 4, 5, 6, and 7.</p> Signup and view all the answers

<p>The binary number 1111 converts to the decimal number 15.</p> Signup and view all the answers

<p>The decimal number 25 can be expressed in hexadecimal as 19.</p> Signup and view all the answers

<p>The binary number system is base 2 and uses two symbols (0 and 1), while the decimal system is base 10 and uses ten symbols (0-9).</p> Signup and view all the answers

<p>The binary representation of 117 is <code>1110101</code>.</p> Signup and view all the answers

<p>'k' in base 2 powers represents 2¹⁰, which equals 1024.</p> Signup and view all the answers

<p>The addition results in <code>101110</code>.</p> Signup and view all the answers

<p>The hexadecimal value of 451 is <code>1C3</code>.</p> Signup and view all the answers

<p>The result is <code>2¹⁶</code>, which equals 65,536.</p> Signup and view all the answers

<p>1327_8</p> Signup and view all the answers

<p>2BB_{16}</p> Signup and view all the answers

<p>Use binary as an intermediary.</p> Signup and view all the answers

<p>1110111</p> Signup and view all the answers

<p>000110101111</p> Signup and view all the answers

<p>110</p> Signup and view all the answers

<p>725_8</p> Signup and view all the answers

<p>17414_8</p> Signup and view all the answers

<p>52_8</p> Signup and view all the answers

<p>F0_{16}</p> Signup and view all the answers

<p>Divide the number by two and track the remainders.</p> Signup and view all the answers

<p>$125_{10} = 1111101_2$</p> Signup and view all the answers

<p>$0.6875_{10} = 0.1011_2$</p> Signup and view all the answers

<p>Multiply each bit by $2^n$, where n is the position index of the bit.</p> Signup and view all the answers

<p>$101011_2 = 43_{10}$</p> Signup and view all the answers

<p>Multiply each digit by $8^n$, where n is the position index starting from 0 on the right.</p> Signup and view all the answers

<p>$724_8 = 468_{10}$</p> Signup and view all the answers

<p>Multiply each digit by $16^n$, where n is the bit's position starting from 0.</p> Signup and view all the answers

<p>This evaluates to $1 imes 16^2 + 10 imes 16^1 + 3 imes 16^0 = 419_{10}$</p> Signup and view all the answers

<p>1631</p> Signup and view all the answers

<p>010 101 111</p> Signup and view all the answers

<p>0011 1011 0111</p> Signup and view all the answers

<p>141_8</p> Signup and view all the answers

<p>0.5_8</p> Signup and view all the answers

<p>710.6_8</p> Signup and view all the answers

<p>FF_{16}</p> Signup and view all the answers

<p>7.1_8</p> Signup and view all the answers

<p>2861</p> Signup and view all the answers

A number system with base 10, using digits 0-9.

A number system with base 2, using digits 0 and 1.

A number system with base 8, using digits 0-7.

A number system with base 16, using digits 0-9 and A-F.

The number of unique symbols used in a number system.

Changing a number from one system (e.g., decimal) to another (e.g., binary).

Converting a binary number to its decimal equivalent.

A method to convert a decimal (base-10) number to a binary (base-2) number.

Method to convert an octal (base-8) number to a decimal (base-10) number.

Method to convert a hexadecimal (base-16) number to a decimal (base-10) number.

The rightmost bit in a binary number.

Transforming numbers from one base (like decimal, binary, octal, or hexadecimal) to another.

Any positive integer power of the number 2.

Any positive integer power of the number 8.

Any positive integer power of the number 16.

A process to convert a decimal number into its octal equivalent. Method involves repeated division by 8 and record remainders

Convert a decimal number to its hexadecimal equivalent, using repeated division by 16 and record remainders.

Convert a hexadecimal number to its binary equivalent by converting each hexadecimal digit into a 4-bit binary.

Convert an octal number to its binary equivalent. Each octal digit translates to a 3-bit binary.

Base-16 Number System using digits 0-9 and A-F to represent values 10-15

Base-8 Number System using digits 0-7

Base-2 Number System using digits 0 and 1

Refers to 2¹⁰ (1024) rather than the standard 1000 in computing, particularly for memory sizes.

In binary addition, when adding two 1 bits, a 'carry-over' of 1 occurs to the next significant digit.

When multiplying exponents with the same base, you add the powers together.

Adding two binary numbers, 11 + 11 results in 110.

Converting a binary number to an octal number by grouping bits in threes and converting each group.

Converting a binary number to a hexadecimal number by grouping bits in fours and converting each group.

Converting octal to hexadecimal using binary as an intermediary.

Converting hexadecimal to octal by using binary as an intermediary.

represents a 3-bit binary value. Examples: 0, 1, 2, 3, 4, 5, 6, 7

Represents 4 binary digits. Examples: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

The standard base-10 number system.