Whenever you see a string of ones and zeros, chances are you're looking at a binary number. In order to make sense of binary numbers, it helps to compare the columns used in the binary system to those used in the decimal system we're all familiar with. Once you have the basics down, you should be able to count from 1 to 1010 without any problem at all. For larger numbers, you can convert the numbers yourself, or use Excel to convert the numbers for you.
Note that even if you prefer to use Excel to read binary numbers, it's important to know how the binary system works, just in case you make an error when setting up a conversion worksheet.
Reading and Understanding Binary
Open an Excel spreadsheet and type the numbers 0 to 10 in a single column. You can do this exercise with pencil and paper, if you prefer.
In the second column, beside each number, type the binary equivalents, which are: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010.
Look at the pattern that emerges when the binary numbers are arranged in a single column.
Decimal numbers are based on 10 basic numbers -- 0 through 9. When we count with decimal numbers, each column can go up only to the number nine. As soon as a column gets to nine, in order to add one, we change the 9 to a zero and add one to the column on the right.
The same rule applies to binary, except there are only two numbers to work with instead of nine -- 0 and 1. When we count in binary, if we want to add one to a column that already has a one, we change it to zero and add one to the column on the left. When all of the columns are full of ones, a new column is added to the left and all of the existing columns turn back to zero. Thus, 1 becomes 10, 11 becomes 100 and 111 becomes 1000.
Write out the columns used to organize decimal numbers as exponents of the number 10 for a deeper understanding of how columns affect how we read numbers. When expressed as exponents, what we call the Hundreds column is actually 10^2, or 10 to the power of 2. The Tens column is 10^1, or 10 to the power of 1, and the Ones column is 10^0. Note that any number expressed as the power of 0 is always 1.
If we look at the number 320, another way to express it is as: (3 x 10^2 ) + (2 x 10^1) + (0 x 10^0) \= 300 + 20 + 0 \= 320
Write down the columns used to organize binary numbers in their exponent values. Because binary is based on only two numbers, each column is expressed as an exponent applied to the number 2. The exponents used in each column, however, are exactly the same as those used in the decimal system. The first column on the left is 2^0, the second column is 2^1 and the third column is 2^2.
If we look at the binary number 111, another way to express it is as: (1 x 2^2 ) + (1 x 2^1) + (1 x 2^0) \= 4 + 2 + 1 \= 7
Use Excel to Read Binary Numbers
Open a new Excel worksheet. In this worksheet, whenever you enter a decimal number in cell B3, cell B4 will convert it to binary. When you enter a binary number in cell B6, Excel will convert that number to a decimal in cell B7.
Click cell "B4" and enter Excel's decimal to binary formula for cell B3: =DEC2BIN((B3))
Type a decimal number in cell B3 and press "Enter. Excel converts this number to the binary equivalent in cell B4.
Click cell "B7." Type the Excel's binary to decimal formula: =BIN2DEC(B6)
Type any binary number in cell "B6." When you press "Enter," Excel converts this to its decimal equivalent.