Activity Guide - Binary Practice


Unit 1 Lesson 7
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Activity Guide - Binary Practice
Background: Number systems help us express and reason about quantities. Early number systems were
merely a system of tallies that allowed humans to record and perform simple arithmetic with values. The
number system we use today uses the concept of place value to allow us to express any value we wish
by combining only 10 symbols (0, 1, 2 …). We therefore call it a “base 10” number system. When
developing a number system for a computer, we only have two symbols available to us, corresponding
with the two states of a single bit. However, the power of place value allows our binary or “base 2”
number system to express any value we wish.
When using this binary representation of numbers, certain values (1, 2, 4, 8, 16, etc.) are seen
repeatedly. When written in binary, these values are 1, 10, 100, 1000, 10000, and so on, and so are the
incremental place values in this binary number system.
Warm-up: In the previous lesson you created numbering systems that allowed you to count from 0 to 26.
The symbols you used were 3-shape permutations of circles, triangles and squares, arranged in an order
by a set of rules you defined. For this activity you will be using only two shapes, which may be familiar.
0 and 1
In other words, you will be building a number system using bits! Note that up until now we’ve called the
two states of our bits A and B. From now on, however, we’ll be calling the two states of a bit 0 and 1.


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