# Octal to Binary, Decimal, Hexadecimal Number System Conversions

Octal number can be converted into 3 number systems.

• Octal to Binary
• Octal to Decimal
Let us discuss all the conversions with simple exampples.

## Octal to Binary

• Step 1:

For each digit of octal number, write the corresponding three bits binary code.

• Step 2:

Combine all the binary bits to get the final result.

```	For example:
To covert the octal number(44.2)8 into binary number.

1. For each digit of octal, write the corresponding 3 bits binary code.

(44.2)8 ====> 100  100 .  010

2. Combine all the binary bits to get the final result.

(A5.1)16 ====> (100100.010)2
```

• Step 1:

For each digit of octal, write the corresponding 3 bits binary code.

• Step 2:

Next, group four bits on the binary number, if there will be one or two or three bits, are left on the group, we need to add the required number of zeros (at the end of both sides) to make them a group.

• Step 3:

Finally, write the corresponding hexadecimal number for that group of four-bit binary code.

```	For example:
To covert the octal number(42.04)8 into hexadecimal number.

1. For each digit of octal number, write the corresponding 3 bits binary code.

(42.04)8 ====>100 010 .  000 100

2. Combine all the binary bits to get the binary number. Then, group three bits on the binary number,

(42.04)8 ====> (100010.000100)2

(42.04)8 ====>  10 0010 . 0001 00 (add zeros on both side)

(42.04)8 ====>  0010 0010 . 0001 0000

3. Finally, write the corresponding hexadecimal number for that group of four-bits binary code.

(42.04)8 ====> (22.10)16 ====> (22.1)16

```

## Octal to Decimal

• Step 1:

First, perform the multiplication of each octal digit with the corresponding positional value.

• Step 2:

Next, add all the products to get the final decimal value.

```	For example:
To covert the octal number(25.2)8 into decimal number.

1. Multiplay each digit of octal with coressponding positional values.

(25.2)8 ====> 2 * 81 + 5 * 80 + 2 * 8-1

2. Add all the products to get the final decimal value.

(25.2)8 ====> 2 * 8 + 5 + 2 / 8

(25.2)8 ====> 16 + 5 + 0.25

(25.2)8 ====> (21.25)10
```

# Octal to Binary, Decimal, Hexadecimal Number System Conversions

Octal number can be converted into 3 number systems.

• Octal to Binary
• Octal to Decimal
Let us discuss all the conversions with simple exampples.

## Octal to Binary

• Step 1:

For each digit of octal number, write the corresponding three bits binary code.

• Step 2:

Combine all the binary bits to get the final result.

```	For example:
To covert the octal number(44.2)8 into binary number.

1. For each digit of octal, write the corresponding 3 bits binary code.

(44.2)8 ====> 100  100 .  010

2. Combine all the binary bits to get the final result.

(A5.1)16 ====> (100100.010)2
```

• Step 1:

For each digit of octal, write the corresponding 3 bits binary code.

• Step 2:

Next, group four bits on the binary number, if there will be one or two or three bits, are left on the group, we need to add the required number of zeros (at the end of both sides) to make them a group.

• Step 3:

Finally, write the corresponding hexadecimal number for that group of four-bit binary code.

```	For example:
To covert the octal number(42.04)8 into hexadecimal number.

1. For each digit of octal number, write the corresponding 3 bits binary code.

(42.04)8 ====>100 010 .  000 100

2. Combine all the binary bits to get the binary number. Then, group three bits on the binary number,

(42.04)8 ====> (100010.000100)2

(42.04)8 ====>  10 0010 . 0001 00 (add zeros on both side)

(42.04)8 ====>  0010 0010 . 0001 0000

3. Finally, write the corresponding hexadecimal number for that group of four-bits binary code.

(42.04)8 ====> (22.10)16 ====> (22.1)16

```

## Octal to Decimal

• Step 1:

First, perform the multiplication of each octal digit with the corresponding positional value.

• Step 2:

Next, add all the products to get the final decimal value.

```	For example:
To covert the octal number(25.2)8 into decimal number.

1. Multiplay each digit of octal with coressponding positional values.

(25.2)8 ====> 2 * 81 + 5 * 80 + 2 * 8-1

2. Add all the products to get the final decimal value.

(25.2)8 ====> 2 * 8 + 5 + 2 / 8

(25.2)8 ====> 16 + 5 + 0.25

(25.2)8 ====> (21.25)10
```