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Binary What?

Paul Cross on Flickr

When you see a letter A on your computer screen, did you know the computer doesn’t actually use the letter A? Instead, it uses a unique string of numbers 01000001 for A. This is called a binary number because it uses two numbers, 0 and 1, to represent the letter A.

Computers transport, calculate, and translate binary numbers because computer hardware circuits only have two electrical states, on or off. These two states can be represented as zero (off) or one (on). All letters of the alphabet, numbers, and symbols are converted to unique eight (or more) character binary numbers as you use software on your computer.

You can have fun with binary numbers without diving deeply into how computers translate unique binary numbers into letters, numbers, and characters.

Here’s how binary numbers work. First, each position in a string of ones and zeroes represents a power of 2. A zero means no value is counted. A one means the value of a power of 2 is added to your total number. The value of the power of 2 depends on the position of the one in the string. A binary number value is calculated by adding up the power of 2 values, working from right to left.

The two-digit binary number 1 1 has a value of 3. The left 1 is in the position with a power of 2 value of 2 while the right 1 is in the position with a value of 1.

1 1 Write a binary number 1 or 0 in each cell
2 1 Position Value (as a power of 2)
2 1 Write value of each 1 then write total here:

2 + 1 = 3

The three-digit binary number 1 1 0 equals 6 (4 + 2):

1 1 0 Write a binary number 1 or 0 in each cell
4 2 1 Position Value (as a power of 2)
4 2 Write value of each 1 then write total here:

4 + 2 = 6

You might ask, what’s a power of 2 number? It’s not a superhero super power. It’s creating a sequence of numbers by multiplying each number by 2 and starting with the number 1. So, 1×2 = 2, 2×2 = 4, 4×2 = 8, onwards. Power of 2 values, therefore, are 1, 2, 4, 8, 16, 32, 64, and really onwards until the end of time.

While Gottfried Leibniz in 1703 published a paper that describes binary numbers, the computer scientist Claude Shannon in 1937 was the first to suggest all electronic data can be reduced to one unit, either on or off. These units are called binary digits or bits. Shannon took Leibniz’s idea and an earlier idea developed by the French mathematician George Boole, about algebra and a theory using two values, and used these ideas to quantify and measure the data that flowed across the US AT&T telephone networks.

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