Counting in Binary
Our standard system of counting involves columns of 10. Once you get to nine, you’ve filled in
the column and have to move on to the next column if you add one more. Therefore, every digit in this
next column counts for ten.
In binary, you only use two digits, zero and one. In this case, once you get to one in a column,
you’ve filled in the column and have to move on to the next column if you add one more. Therefore,
every digit in this next column counts for 2.
Counting in a ‘base ten’ system would work as follows: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Counting in a binary system would work this way: 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010
Instead of the columns being the ones, tens, hundreds, etc- the columns would be ones, twos, fours,
eights, etc.
To convert binary to our standard system, we have to write out the binary number in expanded notation
using the right column ideas.
For Example:
1011= 1x8+0x4+1x2+1x1= 8+0+2+1=11
10101=1x16+0x8+1x4+0x2+1x1=21
11=1x2+1x1=3
Problems:
Write each of the following binary numbers as standard numbers.
a) 1101
b) 110
c) 11111
d) 10
Write out the next three numbers in binary after the given one:
e) 101
f) 1001
g) 10110
h) 1
How big of a number can you create with 5 columns in binary? With 6 columns? 7?