Boolean Functions 101

ComputersAug 2021

Atop the logic gate comes the ability to represent it mathematically. A boolean function gives us that ability. It takes a binary input (either a zero or a one) and returns a binary output.

Take the simple mechanisms AND, OR and NOT. These can be represented using simple expressions. AND maps to multiplication, OR maps to addition, and NOT maps to negation.

Boolean functions are used to describe and conceptualize the binary logic inside a computer chip. Chips are built out of simpler building blocks like AND, OR and NOT.

A boolean function can either be represented as a function:

Or its equivalent truth table. This is an enumeration of all possible inputs and the outputs they map to.

This means that we can construct a truth table out of a boolean function by calculating all possible inputs. But, the reverse is also possible. We can also construct a boolean function out of a truth table.

We do this by [1] isolating all the rows that output 1; [2] constructing a literal expression that represents that particular row of the truth table; and [3] ORing them together. This long boolean function is still an accurate description of the truth table.

This is what is called the canonical representation of a boolean function.

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Coffee shops and anonymity

PersonalAug 2021

What is it about being alone at a coffee shop—about being alone in public, anonymous amidst an audience of strangers? Perhaps, between the anonymity and exposure, we're free to lose a little of who we are and invent a little of what we can become.

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A day at the beach

PersonalAug 2021

The experience of looking down and seeing myself in space and in time. Thirty-three, at this particular beach, surrounded by strangers, each one in our own story. I look up and I see the moon, a reminder that we're floating in space in a small planet. That is a day at the beach.

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Time goes on, unfailingly.

PersonalAug 2021

I feel anxious when I don't draw. If enough time goes by I'll inevitably end up feeling this tingling discomfort. It's easy to overlook where I am and natural the passing of time. For a week to go by as if it had barely happened, for January to have been yesterday. The antidote I keep coming back to is art. To grab a pen, write down the time and place, and acknowledge, with seeing eyes, where I am.

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A private audience with nature

PersonalAug 2021

I go for a walk every morning before starting work. I do so, unfailingly. My own private audience with nature, with the many trees on the way, the flocks of newborn birds chirping in excitement, and the sun as it slowly rises in the horizon. In silence, coffee in hand, in attention.

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These are my dots: An experiment in letting go of my story.

PersonalAug 2021

I do many things, I always have. Drawing is one of them. I have drawn as a way to document my world for years, if not even my entire life, but have done so somewhat in secret. Not out of shame, but, because it doesn't fit into a neat story together with code, design, and my many other curiosities.

But, as of late, I've been practicing giving up control of my story and instead let it unfold as it wants to. Like Jobs said at Stanford in 2005, you can't connect the dots looking forward; you can only connect them looking backwards. You have to trust that the dots will somehow connect in the future.

I make big drawings with thick sharpies, I also make a mean investor pitch deck, I'm currently learning how computers are built all the way down to the lower levels of transistors and boolean logic, I design decent brands, I've read most of Carl Jung's books, and in my job I synthesize products into stories.

These are my dots...

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