# Conversion of Bases to Other Bases

To covert a number from some base to any other given base, first write down that number and then divide it by the given base. We then note the remainder obtained from the division. Ultimately, divide the quotient of the division obtained by the given base. The obtained remainder should be noted. This process needs to be repeated till the quotient happens to be 0. Write the values of the remainders in this process from the bottom to the top. Thus, it will be the answer that is required.

Before you proceed ahead with this concept, check out the basics of conversion to various bases. In this article, we will take a look at the Conversion of Bases to Other Bases according to the GATE Syllabus for CSE (Computer Science Engineering). Read ahead to learn more.

## How to Perform Conversion of Bases to Other Bases?

In the case of number systems, it is very crucial that one has a thorough knowledge of how one can convert various numbers from a given base to another one. In this article, we will learn how one can convert some numbers from any given to any other base.

### Conversion of Bases

A given number in base ‘m’ can be converted to any other base ‘n’ using the given steps below:

#### Step-01

Conversion of the number to base 10 from base m with the help of the expansion method.

#### Step-02

Conversion of the number to base n from base 10 with the help of the division and the multiplication method.

## Practice Problems on Conversion of Bases to Other Bases

1. Convert the given numbers from the first base to the second base-

1.1. (1056)16 to ( ? )8

Answer – We use the expansion method here to convert to base 10, and we get-

(1056)16 â†’ ( ? )10

(1056)16

= 1 x 163 + 0 x 162 + 5 x 161 + 6 x 160

= 4096 + 0 + 80 + 6

= (4182)10

From here, we get (1056)16 = (4182)10

We use the division method here to convert to base 8, and we get-

(4182)10 â†’ ( ? )8

From here, we get (4182)10 = (10126)8

Thus, we get (1056)16 = (10126)8

1.2. (11672)8 to ( ? )16

Answer – We use the expansion method here to convert to base 10, and we get-

(11672)8 â†’ ( ? )10

(11672)8

= 1 x 84 + 1 x 83 + 6 x 82 + 7 x 81 + 2 x 80

= 4096 + 512 + 384 + 56 + 2

= (5050)10

From here, we get (11672)8= (5050)10

We use the division method here to convert to base 16, and we get-

(5050)10 â†’ ( ? )16

From here, we get (5050)10 = (13BA)16

Thus, we get (11672)8 = (13BA)16

1.3. (2724)8 to ( ? )5

Answer – We use the expansion method here to convert to base 10, and we get-

(2724)8 â†’ ( ? )10

(2724)8

= 2 x 83 + 7 x 82 + 2 x 81 + 4 x 80

= 1024 + 448 + 16 + 4

= (1492)10

From here, we get (2724)8= (1492)10

We use the division method here to convert to base 5, and we get-

(1492)10 â†’ ( ? )5

From here, we get (1492)10 = (21432)5

Thus, we get (2724)8 = (21432)5

1.4. (3211)4 to ( ? )5

Answer – We use the expansion method here to convert to base 10, and we get-

(2724)8 â†’ ( ? )10

(3211)4

= 3 x 43 + 2 x 42 + 1 x 41 + 1 x 40

= 192 + 32 + 4 + 1

= (229)10

From here, we get (3211)4= (229)10

We use the division method here to convert to base 5, and we get-

(229)10 â†’ ( ? )5

From here, we get (229)10 = (1404)5

Thus, we get (3211)4 = (1404)5

1.5. (1001001100)2 to ( ? )6

Answer – We use the expansion method here to convert to base 10, and we get-

(1001001100)2 â†’ ( ? )10

(1001001100)2

= 1 x 29 + 0 x 28 + 0 x 27 + 1 x 26 + 0 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 0 x 20

= 512 + 64 + 8 + 4

= (588)10

From here, we get (1001001100)2 = (588)10

We use the division method here to convert to base 6, and we get-

(588)10 â†’ ( ? )6

From here, we get (588)10 = (2420)6

Thus, we get (1001001100)2 = (2420)6

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