# Decimal and Binary Number Systems

If you’re planning on taking the Network+ exam, you need to have a basic knowledge of numbering systems such as decimal. While this is basic knowledge, it is still important. If you haven’t used these numbering system in a while, they might be a little foggy.

For example, see if you can convert the following decimal numbers to four binary bits:

- 1
- 3
- 5
- 9

The answer is available at the end of this post.

### Decimal

When reviewing many topics, it’s worth reviewing what you know and then connecting it to new topics. In this case, you should have a good understanding of decimal. Decimal numbers use a base of ten and include the numbers 0 to 9. Because it’s a base of 10, the next number after 9 is 10.

This shouldn’t be a surprise to anyone reading this book. However, it’s important to understand the underlying details of base 10.

The position of each number within base 10 has a different value such as 1, 10, 100, 1000, and so on. For example, consider the number 2,478. It has four numbers (2, 4, 7, and 8) but these numbers have significantly different values based on their *place*.

- 2 is in the thousands
*place*so it has a value of 2,000 (2 × 1000) - 4 is in the hundreds
*place*so it has a value of 400 (4 × 100) - 7 is in the tens
*place*so it has a value of 70 (7 × 10) - 8 is in the ones
*place*so it has a value of 8 (8 × 1)

I’ve had students in the classroom try to make this difficult, but it doesn’t need to be. Imagine I offered you the choice of receiving $2,478 or $8,742. Which would you choose?

If you’re like most people, you recognize the first number is over $2,000 but the second number is over $8,000. Clearly, you would take the $8,000. The math behind it is that the 8 is in the thousands place so it represents 8 thousand dollars.

The table shows the underlying details using the base 10 number 2,478.

**Base 10 Table**

**Note:** Exams often use the caret (^) character instead of superscript so I’m using the caret here. In other words, 10^2 is the same as 10^{2}.

- Column A is 10^3 or 10 × 10 × 10 (1,000).
- With a value of 2, it equates to 2 × 1,000 (2,000).

- Column B is 10^2 or 10 × 10 (100).
- With a value of 4, it equates to 4 × 100 (400).

Learn more about other number systems such as binary, hexadecimal and octal.

Sign up for the free Networking Components course here.

Here are two important rules to know for any numbering system:

**Any number raised to the power of 1 is itself so 10^1 is 10.**- Column C is 10 ^ 1 (10).
- With a value of 7, it equates to 7 × 10 (70).

**Any number raised to the power of 0 is 1 so 10^0 is 1.**- Column D is 10 ^ 0 (1).
- With a value of 8, it equates to 8 × 1 (8).

## Binary

Binary numbers use a base of 2 and include only the numbers 0 and 1. If you were to count with binary, it would look like this:

- 0
- 1
- 10
- 11
- 100
- 101

Just as decimal numbers have different values depending on their place, binary numbers also have different values depending on their place.

As an example, 2 raised to the power of 2 is the equivalent of 4 decimal (2 squared or 2 × 2). Most people know that 2 × 2 = 4. Similarly, 2 raised to the power of 3 is 8 (2 × 2 × 2). Table 1.2 shows several values for base 2, along with a binary number of 0000 1001.

Just as in base 10, base 2 follows these two rules:

**Any number raised to the power of 0 is 1 so 2^0 is 1.****Any number raised to the power of 1 is itself so 2^1 is 2.**

| A | B | C | D | E | F | G | H |

Base 2 | 2^7 | 2^6 | 2^5 | 2^4 | 2^3 | 2^2 | 2^1 | 2^0 |

Decimal Values | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

Binary Number | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |

Binary Values | 0 | 0 | 0 | 0 | 8 | 0 | 0 | 1 |

** ****Base 2 Table**

- The binary number 0000 1001 has four leading zeros (Columns A, B, C, and D), which can be ignored when calculating the binary value.
- Similarly, the number 5 is the same as 0005. With 0005, we ignore the leading zeros.

- Column E is 2^3 or 2 × 2 × 2 (8).
- With a binary number of 1, it equates to 1 × 8 (8).

- Columns F and G have 0 as the binary number so have a value of zero.
- Column H is 2^0 or 1.
- With a value of 1, it equates to 1 × 1 (1).

From a simpler perspective, the binary number of 0000 1001 equates to a decimal of number 9 (8 + 1).

#### Try This:

See if you can convert the following decimal numbers to four binary bits:

- 1
- 3
- 5
- 9

Answer. The following decimal numbers converted to four binary bits are:

- 1 is 0001
- 3 is 0011
- 5 is 0101
- 9 is 1001

Practice Test Questions To Help You Pass the Network+ Exam (N10-006) The First Time You Take It.