Next

Restart

Back

1

+

–

3/6

1000

14

Binary Systems

3

1110

0100

0

Binary Numbers

7

0011

Click +/-  to change the number.

=

0

Binary Input Switches

4

0000

Binary Output LEDs

12

6

10

15

1100

1001

1111

0111

2

The position of the switches or state of the LEDs can be used to represent small and large numbers. Switches would be used to input binary data while LEDs could be used to output binary data. Let's convert binary numbers to decimal numbers. Use the red and green buttons to count up or count down in binary.  This is how to count to 15 in Binary.

0010

Boolean Algebra

13

1010

1101

0101

9

11

8

0001

5

1011

1

Truth Values

True

Computer scientists and cybersecurity professionals use the binary number system. The ones and zeros can represent switch positions ON (1) or OFF (0) or LEDs ON (1) OFF (0). Binary math is based on the binary number system, a number system that consists of two digits, 1 and 0. The decimal system uses multiples (or powers) of 10. You can represent any number in the decimal system in binary. Like the decimal system, each digit in the binary system represents a value, but these are values based on multiples or powers of 2 not multiples of 10. The first digit on the left of the decimal point in the binary number system is 20, which equals 1. Each preceding digit to the left represents a higher value or power of 2. For examples: 21=2, 22=4, 23=8, 24=16 and so on.

2/6

False

Binary Mathematics

25

4

24

Binary to Decimal Conversion

23

4/6

22

128

2

21

64

20

32

27

16

Like the decimal system each digit in the binary system represents a value, but these values are based multiples or powers of 2 not multiples of 10. So the first digit on the left of the decimal point in the binary number system would represent 20 = 1. Each number preceding digit to the left would represent a higher value or power of 2. For examples: 21=2, 22=4, 23=8, 24=16 and so on and so on.

26

8

.

0.25

2-3

Going to the right is a little different. The first digit to the right of the decimal point would represent 2-1 = ½, then 2-2=1/4, 2-3=1/8, 2-4=1/16 and so on.

0.5

0.125

0.0625

Click switches on and off

1/16

2-4

1/2

2-1

0.00

1/4

DP

6/6

2-2

1/8

Ethics Challenge

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This material was developed with funding from the National Science Foundation

This work is licensed with a Creative Commons Attribution 4.0 International LicenseEndFragment

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Use the eight switches above to represent the binary number between 0 and 255. A switch in the ON posiition represents a binary 1, and a switch in the OFF position represents a binary 0. By turning the switches on and off, you can see the binary equivalent of 0 through 255.

128

64

128