In base-10, place values correspond to powers of 10, for example:

In base-b, place values correspond to powers of b:

### Base-5

Base-5 uses the digits **0, 1, 2, 3, 4** to represent any number. In base-5, we start by counting **1, 2, 3, 4**. At 5, however, we must write 10_{5} (base-5 does not use the digit “5”):

Here’s how we write to up to 10 in base-5.

**Q1. **Convert 4302_{5} to decimal notation.

**Q2. **Write 384 as a base-5 numeral.

**Q3. **Add 342_{5} + 223_{5}

**Q4. **Subtract 424_{5} − 143_{5}

**Q5. **Multiply 134_{5} × 32_{5}

**Q6. **Perform the division 4132_{5} ÷ 23_{5}

### Base-8

The base-8 or octal system uses the digits: **0, 1, 2, 3, 4, 5, 6, 7**. Notice that this time the digit “8” isn’t being used. The counting pattern is:

### Base-16

The base-16 or *hexadecimal system* uses the digits: **0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F**

The counting pattern is:

### Base-2 (Binary)

The base-2 or *binary* system uses the digits: **0, 1**. The counting pattern is:

**Q1.** Write the binary command 1011001101011110 using octal notation.

**Q2.** Write the binary command 1011001101011110 using hexadecimal notation.