T-shirt quote binary numbers

The "On" or "Off" state used in binary is represented by 1 and 0. In the language of your computer there is only 2 words, 2 numbers, 2 characters, 2 states of being, and they are 1 and 0. The reason for this is your computer uses a processor to "think". This processor has millions of transistors. Each of these transistors can either be On or Off.

There is no in between. The dictionary defines Binary as "relating to, using, or expressed in a system of numerical notation that has 2 rather than 10 as a base. Meaning in binary there are only 2 digits instead of Normally we use 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 to express numbers.

The method is very useful but hard to express in computer language. One of my favor T-Shirts says "The are only 10 types of people. Those that understand binary and those that don't. As you can likely figure out from the second sentence in the quote the binary number "10" actually equals "2" in our standard decimal numeric system. How can this be? The following diagrams will help explain how this can be. When you count in our standard decimal numerical system the first digit in a number represents a single quantity.

In this decimal system each new digit is worth 10 times the digit before it. This is an example of base ten math. Binary is a base 2 math system. Thusly, in binary each new digit is worth 2 times the digit before. Let's explore this more. Since the binary system only has 2 digits we can't represent any number higher than 1 without putting a second digit in another column.

This second column however does not equal 10 like in the standard decimal numerical system, it actually equals 2. This fact is why the above quote from the aforementioned T-shirt works.

So let's add one. With this knowledge in mind what about 3. We can now count to 3 using our two available digits and some addition To better illustrate the difference between the binary system and our standard decimal numerical system we should examine the actual value of each column in these different numeric system.

As you can see at the top of this diagram, in the binary system each new column is worth 2 times the previous column instead of 10 time the previous column in the decimal system. So we either have a 1 or a 0 in the first column, in the second column we either have a 2 or a 0, in the third column we either have a 4 or a 0.

Each new column doubles the value of the column before it. The far right column of this diagram shows a traditional Decimal numerical value. With this numbering system we can represent any number possible with only 2 usable digits. The 1 or the 0. To better understand how to figure out what a binary version of a number will be you just have to do simple subtraction. Take for instance the number We know the values of each column so we just have to do some very basic math.

Our number is The 6th column is 32, but the 7th column is 64 so we can't use any number higher than the 6th column. So we have to start with the 6th column and start subtracting. Some jokes are based on stereotypes of mathematicians tending to think in complicated, abstract terms, causing them to lose touch with the "real world". These compare mathematicians to physicists , engineers , or the "soft" sciences in a form similar to an Englishman, an Irishman and a Scotsman , showing the other scientist doing something practical, while the mathematician proposes a theoretically valid but physically nonsensical solution.

First they see two people entering the house. After a while they notice three people leaving the house. The physicist says, "The measurement wasn't accurate. Mathematicians are also shown as averse to making hasty generalizations from a small amount of data, even if some form of generalization seems plausible:.

An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd.

All the sheep in Scotland are black! If I have to show you how to do this, you're in the wrong class" and "Similarly: At least one line of the proof of this case is the same as before.

This category of jokes comprises those that exploit common misunderstandings of mathematics, or the expectation that most people have only a basic mathematical education, if any.

A museum visitor was admiring a Tyrannosaurus fossil, and asked a nearby museum employee how old it was. The joke is that the employee fails to understand the scientist's implication of the uncertainty in the age of the fossil and uses false precision.

A form of mathematical humor comes from using mathematical tools both abstract symbols and physical objects such as calculators in various ways which transgress their intended scope. These constructions are generally devoid of any substantial mathematical content, besides some basic arithmetic. A set of equivocal jokes applies mathematical reasoning to situations where it is not entirely valid.

Many of these are based on a combination of well-known quotes and basic logical constructs such as syllogisms:. Another set of jokes relate to the absence of mathematical reasoning, or misinterpretation of conventional notation:. That is, the limit as x goes to 8 from above is a sideways 8 or the infinity sign, in the same way that the limit as x goes to three from above is a sideways 3 or the Greek letter omega conventionally used to notate the smallest infinite ordinal number.

A number of mathematical fallacies are part of mathematical humorous folklore. Many numbers have been given humorous names , either as pure numbers or as units of measurement. Sagan has been defined as "billions and billions", a metric of the number of stars in the observable universe. The mathematical constant 42 appears throughout the Douglas Adams trilogy The Hitchhiker's Guide to the Galaxy , where it is portrayed as "the answer to the ultimate question of life, the universe and everything".

Calculator spelling is the formation of words and phrases by displaying a number and turning the calculator upside down. Other letters can be used as numbers too with 8 and 9 representing B and G, respectively. A mathematical limerick is an expression which, when read aloud, matches the form of a limerick. The following example is attributed to Leigh Mercer: A dozen , a gross , and a score Plus three times the square root of four Divided by seven Plus five times eleven Is nine squared and not a bit more.

An oft-repeated joke is that topologists cannot tell a coffee cup from a doughnut , [29] since a sufficiently pliable doughnut could be reshaped by a homeomorphism to the form of a cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.

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