In order for a base two number to be four digits long, the first digit should be a one, and then each of the other three digits can be a one or a zero. This gives you 2 x 2 x 2 = 8 numbers.
Nancy,
Go here:
Decimal-Binary-Octal-Hexadecimal Conversions
Enter any positive integer, try 8. Click the button to convert from decimal to binary. You will see our answer is 1000. Base 2 is also referred to as binary. See the math on the chalkboard for why that is. From the comment above, we'd have:
1000 = 8
1001 = 9
1011 = 11
1111 = 15
1010 = 10
1110 = 14
1100 = 12
1101 = 13
Take a look at the math to see how we get that.