Articles with the ‘Fractions’ Tag - Exploring Binary

How to Check If a Number Is a Power of Two

By Rick Regan November 14th, 2008

How can you tell if a number is a power of two?

That’s easy if it’s in the form 2ⁿ, where n is an integer. For example, 2¹², 2⁰, and 2^-37 are powers of two. That is by definition. But what about arbitrary positive numbers like 16,392, 524,288, or 0.00390625? Are they powers of two? Here’s how to tell — if they can be simplified to the form 2ⁿ, they are; if they can’t, they’re not.

Continue reading “How to Check If a Number Is a Power of Two”

Composing Powers of Two Using The Laws of Exponents

By Rick Regan November 14th, 2008

Powers of two can be combined, under the laws of exponents, to create other powers of two. Under these rules, you can multiply powers of two, divide powers of two, or raise a power of two to a power and still get another power of two. You can combine these rules to create complicated expressions, expressions that result in a single power of two. For example,

$\mbox{\footnotesize{\displaystyle {{\left(\frac{2^4 \cdot 2^3}{2^5}\right)}^3 = \: 2^6}}}$ .

The laws of exponents apply generally to any base; two is no different. But since we’re interested in powers of two, we’ll couch them in terms of powers of two. Once we explain the laws in this way, you’ll understand the math behind the example above.

Continue reading “Composing Powers of Two Using The Laws of Exponents”