Modern Computers Are Binary (continued)

Binary (also known as "base 2") is just another way of representing (writing) the same decimal numbers we've come to know and love.

But instead of having our digits represent powers of ten ("ones," "tens," "hundreds," "thousands", etc.), in binary, representation each digit represents another power of two.

Thus, the binary digits (bits, for short) are "ones," "twos," "fours," "eights," "sixteens," and so on:

16s 8s 4s 2s 1s

In decimal form, we represent the number twenty-nine as a combination of decimal digits: namely, as two tens and nine ones, which totals twenty-nine. We write this as

In binary form, too, we need to come up with a combination of the numbers each digit represents that will total twenty-nine.

We can add up to twenty-nine if we have one sixteen, one eight, one four, zero twos, and one one: sixteen + eight + four + one totals twenty-nine. Thus, in binary representation, we could write the number twenty-nine as:

 

11101


And that's all there is to it! This still means "twenty-nine"; it's just represented (written) differently!

This will work for any whole number. No matter how large a whole number is, if you have enough digits, you can represent the number in binary form.

Fractions, however, are another story. As we'll learn later, computers aren't very good at fractions.

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These pages were written by Steven H. VanderLeest and Jeffrey Nyhoff and edited by Nancy Zylstra
©2005 Calvin College, All Rights Reserved

If you encounter technical errors, contact rit@calvin.edu.