basic data types

Data Structures in C for Non-Computer Science Majors

Kirs and Pflughoeft

Basic Data Types

Remember when we first talked about the different combinations of ‘on’ and ‘off’ positions for a given number of light switches:

With 3-bits, there are 8 possible combinations:

000 100001 101010 110011 111

And, with 4-bits, there are 16 possible combinations:

0000 0100 1000 11000001 0101 1001 11010010 0110 1010 11100011 0111 1100 1111

Decimal To Binary


Kirs and Pflughoeft

Basic Data Types

The same sequencing pattern is used to represent numeric values

Decimal Binary

1 12

34

5

67

8

9

0 0

Decimal Binary Decimal Binary

1011

100

101

110111

1000

1001

10 1010 20 1010011 1011 21 1010112 1100 22 10110

13 1101 23 1011114 1110 24 11000

15 1111 25 11001

16 10000 26 1101017 10001 27 11011

18 10010 28 11100

19 10011 29 11101


Kirs and Pflughoeft

Basic Data Types

Is there any way of converting from decimal to binary??Is there any way of converting from decimal to binary??

Yes - The procedure is similar to one which we use all the time.

Suppose you were asked to convert 5,752 seconds to Hours, Minutes, and Seconds. How would you do it????

Because there are 60 seconds to each minute:

Because there are 60 minutes to each hour:

95 95 Minutes Total 60 5752

5700 52 52 Seconds

1 1 Hour Total 60 95

60 35 35 Minutes

So 5,752 Seconds = 1 hour, 35 minutes, and 52 seconds


Kirs and Pflughoeft

Basic Data Types

Check:

* 60 Seconds 5,700 Seconds

+ 52 Seconds

95 Minutes

5,752 Seconds

1 Hour * 60 = 60 Minutes Number Hours Number Minutes

Total Minutes

Secs. Per Minute

Number Seconds

Total Seconds

35 Minutes

Example #2:

Convert 575 Inches to Yards, Feet, and Inches.


Kirs and Pflughoeft

Basic Data Types

Because there 12 Inches in a Foot:

47 Total Feet

12 575 564 11 No. Inches

Because there 3 Feet in a Yard:

15 No. Yards

3 47 45 2 No. Feet

And so there are 15 yards, 2 feet, and 11 inches in 575 inches.

Check: 3 * 15 = 45 + 2 47 * 12 = 564 + 11 = 575 Inches


Kirs and Pflughoeft

Basic Data Types

What does this have to do with converting What does this have to do with converting from decimal to binary??from decimal to binary??

• for hours to minutes or minutes to seconds OR by 12 • for inches to feet OR by 3 • for feet to yardsWe divide by 2

• for decimal to binary

AND keep track of the remainders. Reconstructing the number from LAST to FIRST

Instead of dividing by 60


Kirs and Pflughoeft

Basic Data Types

Take, for example, the number 1110 (which we know is 10112)

52 11 10 1

22 5 4 1

12 2 2 0

02 1 0 1

• FIRST, Divide 11 by 2:• NEXT, Let the quotient become the new Dividend• CONTINUE Until the Quotient is Zero (0)• FINALLY, Collect the remainders from Last to First

1 0 1 12 = 11 (Check the Table)


Kirs and Pflughoeft

Basic Data Types

2 28

(The notation used varies slightly to save space)

Quotient Remainder (If Even = 0; If Odd = 1)

0

2 14 0

2 7 1

2 3 1

2 1 1

The New Quotient is Zero: Quit

Collecting Remainders from last to first:

The Binary Value is:

1 1 1 0 02

Example 2: Convert 2810 to binary (= 111002):


Kirs and Pflughoeft

Basic Data Types

Example 3: Convert 4410 to binary:

44/2 = 22

The notation used differs to correspond to c syntax: / Integer Division: The result is the quotient % Modulus Arithmetic: The Result is the Remainder

44 % 2 = 022/2 = 11 22 % 2 = 011/2 = 5 11 % 2 = 1 5/2 = 2 5 % 2 = 1 2/2 = 1 2 % 2 = 0 1/2 = 0 1 % 2 = 1

Since the New Quotient is 0: STOP

Collecting from Last to First:

1 0 1 1 0 02


Kirs and Pflughoeft

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