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Binary Challenge

4

24

Binary to Decimal Conversion-Integers

23

2/11

22

128

2

21

64

1

20

32

27

16

Like the decimal system each digit in the binary system represents a value, but these values are based on the power of 2. The first digit left of the decimal point in the binary number system would is 20 which equals 1. Each position continuing on to the represents a higher value or power of 2.

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8

Ethics Challenge

This material was developed with funding
from the National Science Foundation

Binary Challenge

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

1/11

0.5

0

0.25

Click switches on and off

+

.

2-1

5/11

Use the eight switches above to represent binary integer and decimal numbers. 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 integer and decimal equivalents.

0.125

DP

2-2

2-3

2-4

=

1/2

1/8

8

1

1/4

1/16

0.0625

4

0.00

8

Binary to Decimal-1

Binary Value

1010 1100 =

1011 1001 =

6/11

1100 0011 =

0100 0001 =

1111 0111 =

Decimal Value

Element
with Audio
HTML

1001 0110 =

124 =

99 =

Binary Value

254 =

60 =

7/11

224 =

Decimal to Binary-1

29 =

0.0011 =

0.0110 =

8/11

0.0111 =

0.0100 =

0.1100 =

Binary to Decimal-2

0.1001 =

Binary Value

0.25 =

9/11

Binary Value
(use four(4) decimal places in your answer)

0.0625 =

0.9375 =

Decimal to Binary-2

0.875 =

0.625 =

0.5 =

1011.1110 =

1100.0010 =

10/11

0100.1000 =

1011.0011 =

1111.0111 =

Binary to Decimal-3

1001.1100 =

2-7

= 0.5390625

0.5 + 0.125 + 0.0078125

0.015625

2-5

1/32

1/128

2-3

Binary to Decimal Conversion - Decimals

0.03125

0.125

0.0078125

.1 0 1 0 0 0 1

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

0.0078125

2-6

2-1

2-2

2-4

1/64

3/11

5.5 =

12.625 =

Decimal to Binary-3

8.0625 =

14.875 =

15.6875 =

11/11

13.9375 =

4/11

128

64

Use the eight switches above to represent a binary number between 0 and 255. A switch in the ON position 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 the decimal values 0 through 255.

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