# unit 2 task: numbering systems

## Project Description:

recall that the binary numbering system has two symbols (0-1); decimal has ten (0-9), and hexadecimal has sixteen (0-9, a-f). binary numbers should always be written out in sets of four digits each time. each binary digit is called a “bit”. eight bits make up a byte and four bits are a nibble. each hex digit represents one nibble.

for this task, complete the three sections below in a separate document and submit via the instructions at the bottom of the page. be sure to name your file: firstname_lastname_cis106_u2_task1.docx

hint: use the scientific calculator on your computer (calc.exe) to check your work; click on view – scientific in xp, or view – programmer in windows 7. watch the scientific calculator video located in the course materials and resources area of this course to learn more about using the calculator.

part a: counting in binary, decimal, and hexadecimal. fill in the symbols and digits below.

binary

decimal

binary

decimal

0000

0

0

8

1

9

2

1010

10

a

3

11

4

12

5

13

6

14

0111

7

7

15

part b: binary to decimal and hexadecimal. complete the chart. add h to each hex number. fill in the power of 2’s as well. *2^ means “2 to the power of”; for example, 2^5 = 2 * 2 * 2 * 2 * 2 = 32

no.

binary
(1 byte format)

128

64

32

16

8

4

2

1

decimal

hexa-decimal

27

26

25

24

23

22

21

20

1

11001100

1

1

0

0

1

1

0

0

128+64+8+4=204

cch

2

10101010

3

11100011

4

10110011

5

00110101

6

00011101

7

01000110

8

10110001

9

11000001

10

11110000

part c: decimal to binary: complete the following table to practice converting a number from decimal notation to binary format and hexidecimal. mark each hexadecimal number with h.

no.

decimal

128

64

32

16

8

4

2

1

11

49

0

0

1

1

0

0

0

1

32+16+1= 49; 0011=3;0001=1

31h

12

15

13

77

14

140

15

252

16

222

17

192

18

169

19

127

20

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