Lesson 3, Topic 1
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# Number Base

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### Counting in Base 10: (Decimal)

The usual system of counting is called the decimal or denary system.

“dec “means ten which means our usual decimal system is in Base 10.

In Base 10 we have digits for the numbers 0 – 9. We do not have a single digit for ten.

We saw in the previous lesson that the Romans had a single character for 10 which is X.

In Base 10, we write 10 for the number ten, but this stands for 1 ten and 0 ones. This is two digits; we have no single solitary digit that stands for “ten”.

We count in Base 10 like this:

This system enables us to write small or large numbers using a combination of digits.

Numbers in base 10 are usually written without the subscript ten or 10

431 ten is simply written as 431.

Apart from base 10, numbers are counted in other bases such as base two, base five, base seven, base eight, etc.

For example, 64eight means 64 in base 8.

### Counting in Groups of Twos: (Binary)

Binary numbers are numbers written using only 0s and 1s.

Numbers 2, 3, 4, 5, 6, 7, 8, and 9 do not exist in binary.

A major difference between decimal numbers are binary numbers is that decimal numbers are in base 10 and binary numbers are in base 2.

To show that a number is a binary number, follow it with a little 2 like this: 1012. This way people won’t think it is the decimal number “101” (one hundred and one).

As discussed in base 10 there are ten numbers: we count 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

In base 2 we have two numbers: we count 0, 1

How do we Count in Base 2?

In the base 2 number system, we also count in groups of 2

When counting we go to a new group each time we reach a number that is a power of 2.

We, therefore, count as follows:

If we add another object, we have 2 groups of two, which is 4. We continue counting as follows:

If we add another object, we have 3 groups of two, which is 8. We continue counting as follows:

### Decimal vs. Binary

10 as a decimal number is 1010 as a binary number

5 as a decimal number is 101 as a binary number

The four most commonly used number systems are;

1. Decimal Number System
2. Binary Number System
3. Octal Number System
4. Hexadecimal Number System

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