Showing n! > 2n When n Is A Power of Two

Which is bigger, 64! or 264? 64! is, because it follows from a proof by induction for any integer n greater than or equal to 4. It’s also easy to just reason that 64! is bigger: 264 is 64 factors of 2, whereas 64! has 64 factors, except all but one of them (1) are 2 or greater.

When I saw this problem though I wondered if I could solve it in another way: Could the factors of two alone in 64! be greater than 264? As it turns out, almost.

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Hexadecimal Numbers: Uppercase or Lowercase?

Do you prefer hexadecimal numbers written with uppercase letters (A-F) or lowercase letters (a-f)?

For example, do you prefer the integer 3102965292 written as B8F37E2C or b8f37e2c? Do you prefer the floating-point number 126.976 written as 0x1.fbe76cp6 or 0x1.FBE76Cp6?

I ran this poll on my sidebar, and after 96 responses, about 70% are “prefer uppercase” and about 9% are “prefer lowercase”. What do you think? (For the “depends on context” answer I meant things other than numeric values, like the memory representation of strings. However, for the purposes of this article, please answer with just numeric values in mind.)

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Another NaN In the Wild

I see these from time to time, but I don’t always capture them; here’s one I saw recently while playing a podcast:

A NaN in an ad in the app Castbox (partial image)
A NaN in an ad in the app Castbox (click for full image).

(According to Castbox, this is an error in the ad and is out of their control.)

A Simple Binary To Decimal Converter App In Jetpack Compose

I’ve been learning Jetpack Compose and Kotlin (and Android for that matter) so I decided to create a simple binary conversion app to demonstrate how easy it is to create (at least basic) UI in Compose.

https://www.exploringbinary.com/wp-content/uploads/Android.ByteValueOfDecimal67.png
Byte to Decimal Converter Demo App (Pixel 4 Emulator)

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