Decimal (base-10) to hexadecimal (base-16) conversion:

Step 1: Divide the decimal number by 16 (16 comes from the base value of hexadecimal number system).

Step 2: The remainder is the LSD (least significant digit) of the hexadecimal number.

Step 3: Divide the quotient from*Step 1* by 16 again.

Step 4: The new remainder from*Step 3* is the next digit (from right to left) of the hexadecimal number.

Step 5: The process continues until we get 0 as the quotient. The remainder from this step is the MSD (most significant digit) of the hexadecimal number.

Step 2: The remainder is the LSD (least significant digit) of the hexadecimal number.

Step 3: Divide the quotient from

Step 4: The new remainder from

Step 5: The process continues until we get 0 as the quotient. The remainder from this step is the MSD (most significant digit) of the hexadecimal number.

Decimal number: 45_{10}

Numerator | Denominator | Quotient | Remainder |
---|---|---|---|

45 | 16 | 2 | 13 (LSD) |

2 | 16 | 0 | 2 (MSD) |

We know from [Digital Number Systems - Introduction] that 13_{10} = D_{16}

So, the hexadecimal representation: 2D_{16}

So, the hexadecimal representation: 2D

Hexadecimal (base-16) to decimal (base-10) conversion:

From right (LSB) to left (MSB) we will take each digit and multiply them by 16^{x} and later add the results together. Here x is the corresponding position of a digit and 16 comes from the base value of hexadecimal number system.

Hexadecimal number: 2D_{16}

Number: | 2 (MSB) | D (LSB) |
---|---|---|

Position: | 1 | 0 |

We know, D_{16} = 13_{10}

Now, (2 x 16^{1}) + (13 x 16^{0})

= 32 + 13

= 45

So, the decimal representation: 45_{10}

Now, (2 x 16

= 32 + 13

= 45

So, the decimal representation: 45