DE: Activity 1.2.3 Binary Number System

DE: Activity 1.2.3 Binary Number System

Have you ever wondered why we use the base-ten, or decimal, number system? Of course—we have ten fingers. However, the decimal number system that works so well for us is completely incompatible with digital electronics.

Digital electronics only understands two states, ON and OFF. This is why digital electronics use the base-two, or binary, number system. For you to be able to design digital electronics, you need to be proficient at converting numbers between the decimal and binary number systems.

In this activity you will learn how to convert numbers between the decimal and binary number systems.

_{Complete this in your engineering notebook.}

_{Complete this in your engineering notebook.}

Open Ended

The decimal number system has served humans well since the beginning of mankind. Ug the caveman didn’t call it the decimal number system, but he undoubtedly used his fingers to count objects in his world. If the decimal system is so good, why do computer and other digital electronic devices use the binary number system?

Open Ended

Because we are using a number system other than the decimal, it is important to properly subscript our numbers (for example, 3510, 23410, 100102). Why is this so important? Provide at least three examples where neglecting to subscript numbers could lead to confusion.

Open Ended

Without performing the binary-to-decimal conversions, which of the following two binary numbers is the larger number?101101 (2)011010 (2) 101101 (2) 011010 (2)

Open Ended

How were you able to determine which was the larger number?

Open Ended

Perform the binary-to-decimal conversions and check your answer. Were you correct?

Open Ended

Examine the table that you completed in the procedure portion of the activity. What do you notice about the LSB (least-significant-bit)? What do you notice about the middle bit? What do you notice about the MSB (most-significant-bit)? Do you see a pattern?

Based on your observations above, complete the table in your engineering notebook.