# How many bit strings of length 8 begin and end with a 1?

**How many bit strings of length 8 begin and end with a 1**? My answer would be: 26. Because we know, that the

**bit starts**with

**1**and

**ends**with

**1**: Which means, that 2 of the

**length 8**is used, also there are 6 positions remaining, which is 26=64.

Keeping this in consideration, how many bit strings of length 8 either start with a 1 or end with a 00?

Number of bit strings of length 8 that start with 1 and end with 00: 25 = 32. Applying the subtraction rule, the number is **128** + 64 − 32 = 160.

Also Know, how many bit strings of length 8 or less are there? There are 28 which is 256. That means there are 256 different values you can store in a byte, since a byte is eight bits. There are **256 eight**-bit ascii codes, for instance.

Also question is, how many bit strings of length 10 begin and end with a 1?

We are asked about 10 bits, but the first and the last bits are already chosen for us. Bits are either 1 or 0, so there are 2 choices per bit, and 8 bits to choose. Therefore, there are 28 = **256 bit strings** of length ten that begin and end with a 1.

How many six bit strings are there that begin with 01?

Similarly, **there** are 26 **bit strings** that end with **01**. The sum 27+26 double-counts the **bit strings** that **start** with 1 and end with **01**. **There** are 25 of these, so **there** are 27+26−25 **bit strings** that **start** with 1 or end with **01**.