1. Lab 01:Binary numbers, UP-1 switches, and UP-1 LED’s :
Binary Number System:
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Decimal Numbers:
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Binary Number Conversion:
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Switches and LED’s:
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2. 1 9 1 1 1 1 1 1 1 Lab 01 : Binary Number System:
We will use a car odometer to learn about the binary number system. A car odometer (non-digital) consists of a series of plastic discs that rotate to track the distance traveled by a car. 1 9
Driver Viewing Window
A decimal odometer has the outer edge of each disc numbered from 0 … 9. Three discs will allow the odometer to record a maximum distance traveled of 999 Km’s.
A binary odometer has the outer edge of each disc numbered with only 0 and 1. Using 3 discs will allow the odometer to record a maximum distance traveled of 111 binary Km’s … or … 7 km’s. Proceed to watch the odometer in action. 1 1 1 1 1 1 1
Decimal
Equivalent 1 2 3 4 5 6 7
3 Bit Binary
From the odometer example, you can place the 3 bit numbers in a table and see the order of the first 8 binary numbers.
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3. Lab 01 : Decimal Numbers :
Reviewing some fundamental facts about the decimal number system will help you learn the binary number system.
The decimal positional weight chart (PWC).
Each numeral of a decimal number occupies a position that has a weight. Here is the decimal PWC.
Hundreds
Thousands
Tens
One’s
100
101
102
103
10-1
10-2 2 3 5
5 one’s
3 tens
2 Hundreds
The weight of each position have been given names.
A decimal point is used to separate the whole part and the fractional part of a number.
Here is the decimal number 235 placed in the PWC.
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4. Lab 01 : Binary Number Conversions :
Digital systems process data in binary format. It is important to know how to convert back and forth from binary to decimal.
Binary numbers are part of a base 2 number system. Only two numerals exist: 1 and 0.
Converting binary to decimal:
Drop the binary number into the binary PWC to convert it to decimal. Example convert 1101 to decimal. 20 21 22 23 1 2 4 8
… Or …
Binary PWC 1
= 1x8 + 1x4 + 0x2 + 1x1 = = 13
Converting decimal to binary: Example: convert 25 to binary
Write down a binary PWC which the MSB (most significant bit) surpasses the number you are trying to convert.
Work from MSB and use a 1 to include the bit position and a 0 to exclude it. The included bits should have their weight add up to the number being converted.
Exclude because will exceed 25.
Include because will equal 25.
Exclude because will exceed 25.
Include because does not exceed 25.
Include because 16 does not exceed 25. 1 2 4 8 16 32
Exclude because it would make number larger than 25 1 1 1
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5. Lab 01 : Switches and LED’s:
Students can create and test digital systems by using switches to represent binary input data and using LED’s (light emitting diode) to represent binary output data.
Digital systems have an input side and an output side. Each arrow is a connection wire.
The inputs of a digital system are binary digits (bits). You either input a binary 1 (logic 1) or a binary 0 (logic 0). The digital system processes the signals you have applied to the input and responds with binary 1 or binary 0 at the output(s).
5 volts represents a logic 1 and a 0 volts (also called GROUND or Gnd) represents a logic 0. The digital system is powered up by a 5 Volt power supply.
A switch can be used to input a logic 1 and logic 0. An LED can be connected to the output to see the digital system’s response. Continue and you will see the switch and LED in action. 5v 5v
Digital System
Input
Output
Logic 1 ON
Logic 0
OFF
Logic 0
OFF
Logic 0
OFF
Logic 1 ON
Logic 1 ON
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