**Important Computer Awareness Materials (Day-24) – Introduction of Computer Number System (part-2)**:

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__Introduction of Computer Number System (part-2)__

There are many methods or techniques which can be used to convert numbers from one base to another. We’ll demonstrate here the following:

**Decimal to Other Base System:**

**Steps**

**Step 1 – **Divide the decimal number to be converted by the value of the new base.

**Step 2 –** Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number.

**Step 3 –** Divide the quotient of the previous divide by the new base.

**Step 4 –** Record the remainder from Step 3 as the next digit (to the left) of the new base number.

Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3.

The last remainder thus obtained will be the most significant digit (MSD) of the new base number.

__Example:__

Decimal Number: 29_{10}

Calculating Binary Equivalent:

As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the least significant digit (LSD) and the last remainder becomes the most significant digit (MSD).

Decimal Number: 29_{10} = Binary Number: 11101_{2}.

**Other base system to Decimal System:**

**Steps**

**Step 1 –** Determine the column (positional) value of each digit (this depends on the position of the digit and the base of the number system).

**Step 2 –** Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.

**Step 3 –** Sum the products calculated in Step 2. The total is the equivalent value in decimal.

__Example:__

Binary Number: 11101_{2}

Calculating Decimal Equivalent:

**Other Base System to Non-Decimal System:**

**Steps**

**Step 1 –** Convert the original number to a decimal number (base 10).

**Step 2 –** Convert the decimal number so obtained to the new base number.

__Example:__

Octal Number: 25_{8}

Calculating Binary Equivalent:

**Shortcut method – Binary to Octal:**

**Steps**

**Step 1 –** Divide the binary digits into groups of three (starting from the right).

**Step 2 –** Convert each group of three binary digits to one octal digit.

Example

Binary Number: 10101_{2}

Calculating Octal Equivalent:

**Shortcut method – Octal to Binary:**

**Steps**

**Step 1 –** Convert each octal digit to a 3 digit binary number (the octal digits may be treated as decimal for this conversion).

**Step 2 –** Combine all the resulting binary groups (of 3 digits each) into a single binary number.

__Example:__

Octal Number: 25_{8}

Calculating Binary Equivalent:

**Shortcut method – Binary to Hexadecimal:**

**Steps**

**Step 1 –** Divide the binary digits into groups of four (starting from the right).

**Step 2 –** Convert each group of four binary digits to one hexadecimal symbol.

__Example:__

Binary Number: 10101_{2}

Calculating hexadecimal Equivalent:

**Shortcut method – Hexadecimal to Binary:**

**steps**

**Step 1 –** Convert each hexadecimal digit to a 4 digit binary number (the hexadecimal digits may be treated as decimal for this conversion).

**Step 2 –** Combine all the resulting binary groups (of 4 digits each) into a single binary number.

__Example:__

Hexadecimal Number: 15_{16}

Calculating Binary Equivalent:

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