# Conversion of Number Bases explained with examples

#### Academic Questions in MathematicsPlease check out our Test Your Knowledge page to see all Questions and Answers Slanted or tilted lines that will finally meet at some point but NOT at a right angle are referred to as _____. A. oblique B. curved C. vertical D. perpendicular E. parallel F. horizontal The two sides that forms an angle are referred to as the _____. A. arms B. vertexes C. bays D. zones E. limbs F. dune The point where the two sides of an angle meet is termed the _____. A. arms B. vertex C. bays D. zones E. limbs  F. dune How many digits are there in -223.00 A. 1 B. 2 C. 3 D. 4 E. 5 F. 6 30% of 2 is equal to _____. A. 30 B. 0.6 C. 75 D. 0.25 E. 0.3 F. 60

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### Conversion of Number Bases:

In order to convert a base to another base; for instance, if we were to convert a base 10 to base 2, we will first need to know the powers of the base to which we are converting to.

The instances below shows the powers of various numbers:

The powers of 2 are:

• 2 raised to power 0 = 1. (That is; 20 = 1)
• 2 raised to power 1 = 2. (That is; 21 = 2) or (2 x 1 = 2)
• 2 raised to power 2 = 4. (That is; 22 = 4) or (2 x 2 = 4)
• 2 raised to power 3 = 8. (That is; 23 = 8) or (2 x 2 x 2 = 8)
• 2 raised to power 4 = 16. (That is; 24 = 16) or (2 x 2 x 2 x 2 = 16)
• 2 raised to power 5 = 32. (That is; 25 = 32) or (2 x 2 x 2 x 2 x 2 = 32)
• And so on.

Any value raised to the power of zero will always equal to 1.

Simply put, the power of 2 can be written as:

• 1, 2, 4, 8, 16, 32, 64, 128, 256 and so on.

Following the same steps as above, the power or 3 will be:

• 1, 3, 9, 27, 81, 243, 729 and so on.

Still following the same steps as above, the powers of 4 are:

• 1, 4, 16, 64, 256, 1024 and so on:

Note: During the final step of our base conversion, the value "one" (1) divided by our base value of interest will always result in the answer "zero remainder one" (0 remainder 1). This is an important step to note as we shall see in our examples below.

#### Example 1

• Convert the decimal 10 to base 2

Step 1: We need divide the decimal number by the base we want to convert to.

• Decimal value = 10
• We are converting to base 2
##### 10/2 = 5 Remainder 0

Note: We must take into account the remainder from our division because it will be used as our answer.

Every other step will be similar to step 1 but we will divide our resultant answer from the subsequent steps.

Step 2: Our previous answer from the above division was 5

##### 5/2 = 2 Remainder 1

Step 3: Our previous answer from the above division was 2

##### 2/2 = 1 Remainder 0

Step 4: Our previous answer from the above division was 1

##### 1 divided by 2 = 0 Remainder 1

Once our division equals 0, we are done.

Next; we will have to write the reminder from bottom - top; and that’s our answer.

OR

We can also solve this question by using a table; where we will divide the decimal number by the base we want to convert to:

 Base 2 Decimal value Remainder 2 10 - 2 5 0 2 2 1 2 1 0 2 0 1

Counting our remainder from below;

Note: I will use different expressions for the questions below but they will all mean the same thing. (We will be converting a number from base 10 to another base).

#### Example 2

• Convert 15 to base 2

For simplicity, we will use a table to solve this question.

 Base 2 Decimal value Remainder 2 15 - 2 7 1 2 3 1 2 1 1 2 0 1

Counting our remainder from below;

#### Example 3

• Convert 16 to 164
 Base 4 Decimal value = 16 Remainder 4 16 - 4 4 0 4 1 0 4 0 1

Counting our remainder from below;

#### Example 4

• Convert 1610 to base 1616
 Base 16 Decimal value = 16 Remainder 16 16 - 16 1 0 16 0 1

Counting our remainder from below; Alfred Ajibola is a Medical Biochemist, a passionate Academician with over 7 years of experience, a Versatile Writer, a Web Developer, a Cisco Certified Network Associate and a Cisco CyberOps Associate.

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