C for Engineers and Scientists: An Interpretive Approach Number Systems …staff.iium.edu.my/farahhani/index_files/ECE 1322_W1_L2_supplemen… · For example, the octal value 45761023

Created by Harry H. Cheng, 2009 McGraw-Hill, Inc. All rights reserved.

C for Engineers and Scientists: An Interpretive Approach

Number Systems,

Scalar Types, and Input and Output

Outline: Binary, Octal, Hexadecimal, and Decimal Numbers Character Set Comments Declaration Data Types and Constants Integral Data Types Floating-Point Numbers



Binary, Octal, Hexadecimal, and

Decimal

• Binary Binary numbering system has only two possible values for each digit: 0 and 1.

For example,

binary number decimal number

0 0

1 1

10 2

11 3

100 4

101 5

110 6

1100 1010 202



Decimal Numbers

• Decimal The digits' weight increases by powers of 10. The weighted values for

each position is determined as follows:

For example,

A decimal number 4261 can be thought of as follows.

4 * 1000 + 2 * 100 + 6 * 10 + 1 * 1

= 4000 + 200 + 60 + 1

= 4261 (decimal)

104 103 102 101 100

10000 1000 100 10 1



Binary, Octal, Hexadecimal, and

Decimal

• Binary

The digits' weight increases by powers of 2. The weighted values for each position is

determined as follows:

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

For example,

binary 10 is decimal 2.

the binary value 1100 1010 represents the decimal value 202.

1 * 128 + 1 * 64 + 0 * 32 + 0 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 0 * 1

= 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0

= 202 (decimal)



Binary Two‟s Complement

The left-most bit is the sign bit. If it is 1, then the number is negative.

Otherwise, it is positive. Give a negative value, represent it in binary two‟s

complement form as follows.

1. write the number in its absolute value.

2. complement the binary number.

3. plus 1.

Example, represent –2 in binary two‟s complement with 16 bits for short int.

• Binary value of 2: 0b0000 0000 0000 0010

• Binary complement of 2: 0b1111 1111 1111 1101

• Plus 1: +1

• Binary two‟s complement representation of -2: 0b1111 1111 1111 1110



Give binary two‟s complement form of a negative number, find

the absolute value of the negative value as follows.

1. Complement the binary number.

2. Plus 1.

Example, find the decimal value of (0b1111 1111 1111 1110)2 in binary

two‟s complement form with 16 bits.

• Binary two‟s complement (0b1111 1111 1111 1110)2

• Binary complement (0b0000 0000 0000 0001)2

• Plus 1 +1

• Absolute value: (0b0000 0000 0000 0010)2 = 210

• Negative value: -2



Subtraction of a value in the computer can be treated as addition of its

two‟s complement. For example, the subtraction of (2-2) can be

performed as 2+(-2) as follows:

0b0000 0000 0000 0010 (binary representation of 2)

0b1111 1111 11111110 (two‟s complement representation of -2)

0b0000 0000 0000 0000 (2+(-2))



• Example

> short i, j

> i = 0b0000000000000010

2

> j = 0b1111111111111110

-2

> i+j

0



• Octal

The octal system is based on the binary system with a 3-bit boundary. The octal

number system uses base 8 includes 0 through 7. The weighted values for each

position is as follows:

83 82 81 80

512 64 8 1

1. Binary to Octal Conversion • Break the binary number into 3-bit sections from the least significant

bit (LSB) to the most significant bit (MSB).

• Convert the 3-bit binary number to its octal equivalent.

For example, the binary value 1 010 000 111 101 110 100 011 equals to

octal value (12075643)8.



2. Octal to Binary Conversion

• Convert the octal number to its 3-bit binary equivalent.

• Combine all the 3-bit sections.

For example, the octal value 45761023 equals to binary value

100 101 111 110 001 000 010 011.

3. Octal to Decimal Conversion

To convert octal number to decimal number, multiply the value in each position

by its octal weight and add each value together. For example, the octal value

(167)8 represents decimal value 119.

1*64 + 6*8 + 7*1 = 119



• Hexadecimal

Similar to octal, the hexadecimal system is also based on the binary system but

using 4-bit boundary. The hexadecimal number system uses base 16 including

the digits 0 through 9 and the letters A, B, C, D, E, and F. The letters A through F

represent the decimal numbers 10 through 15. For the decimal values from 0 to 15,

the corresponding hexadecimal values are listed below.

15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

F E D C B A 9 8 7 6 5 4 3 2 1 0

Decimal

Hexadecimal



The weighted values for each position is as follows:

163 162 161 160

4096 256 16 1

The conversion between binary value and hexadecimal value is similar to octal

number,but using four-bit sections.

The hexadecimal value 20A represents decimal value 522.

2*256 + 0*16 + 10*1 = 522



Following table provides all the information you need to convert from one type

number into any other type number for the decimal values from 0 to16.

Binary Octal Decimal Hex Binary Octal Decimal Hex

0000 00 00 00 1001 11 09 09

0001 01 01 01 1010 12 10 A

0010 02 02 02 1011 13 11 B

0011 03 03 03 1100 14 12 C

0100 04 04 04 1101 15 13 D

0101 05 05 05 1110 16 14 E

0110 06 06 06 1111 17 15 F

0111 07 07 07 10000 20 16 10

1000 10 08 08



Character Set

The character set in C includes the following members:

– the 26 uppercase letters of the Latin alphabet

A B C D E F G H I J K L M

N O P Q R S T U V W X Y Z

– the 26 lowercase letters of the Latin alphabet

a b c d e f g h i j k l m

n o p q r s t u v w x y z

– the 10 decimal digits

0 1 2 3 4 5 6 7 8 9

– the following 31 graphic characters

! " # % & ' ( ) * + , - . / :

; < = > ? [ \ ] ^ _ { | } ~ $ `



Comments

Comments of a C program can be enclosed within a pair of delimiters /* and */.

The symbol // will comment out a subsequent text terminated at the end of

a line. For example,

/* This is a comment */

/* This is a comment

across multiple lines */

printf(”Hello, world\n”); // This is a comment terminated at the end of line



– An identifier for a variable shall consist of lowercase and uppercase letters,

underscore _, and digits. It shall not start with digits.

– A variable has to be declared before it can be used inside a program. The following format can be used to declare a variable of simple type.

dataType varName;

where dataType is one of valid data types and varName is an identifier.

int main() {

int i;

i = 90;

int j;

j = 20;

return 0;

}

Declaration



• Integer Data Types

Integer is a basic data type and can be represented by one of the

following data types.

char long long

signed char signed long long

unsigned char unsigned long long

short

signed short

unsigned short

int

signed int

unsigned int

long

signed long

unsigned long

Data Types and Constants



> int i

> sizeof(int)

4

> sizeof(i)

4

> sizeof(2*i)

4

> sizeof(long long)

8

The sizeof operator gives the size of types or expression in bytes.

One byte equals 8 bits.



• Int Data Representation

– An int data is a signed integer. An int number is a whole number

that can be negative, positive, or zero.

– An int data uses 4 bytes for storage with 1 bit for the sign.

– The int ranges from INT_MIN to INT_MAX, which are

–2147483648(–231) and 2147483647(231–1), respectively.

– The unsigned int ranges from 0 to UINT_MAX, which is equal to 4294967295(232–1).

INT_MAX 0b01111111 11111111 11111111 11111111

INT_MIN 0b10000000 00000000 00000000 00000000

UINT_MAX 0b11111111 11111111 11111111 11111111



#include <stdio.h>

#include <limits.h>

Int main() {

printf(”INT_MAX = %d\n”, INT_MAX);

printf(”INT_MIN = %d\n”, INT_MIN);

printf(”UINT_MAX = %d\n”, UINT_MAX);

return 0;

}

Output:

INT_MAX = 2147483647

INT_MIN = -2147483648

UINT_MAX = 4294967295

Program: limits.c



• Short Data Representation

– A short data uses 2 bytes for storage.

– The macros for minimum and maximum values of signed short are SHRT_MIN and SHRT_MAX defined in header file limits.h. SHRT_MIN is equal to -32768(-215) and SHRT_MAX is equal to 32767(215-1).

– The macro USHRT_MAX, defined in the header file limits.h, specifies the maximum value of unsigned short. It is equal to 65535(216-1).



• Long Long Data Representation

– Data of long long integral type contains 8 bytes. They have the

similar representation as the data type of int.

– The long long int ranges from LLONG_MIN to LLONG_MAX,

which are -9223372036854775808LL (-263) and

9223372036854775807LL (263–1), respectively.

– The long long int ranges from 0 to ULLONG_MAX, which is 264–1.



• Integer Constants

– An integer can be specified in decimal, binary, octal, or hexadecimal.

– A leading 0(zero) on an integer constant indicates an octal integer.

– A leading 0x or 0X indicates a hexadecimal integer.

– A leading 0b or 0B indicates a binary integer (in Ch only). •

Example:

30 (decimal) = 036 (octal)

= 0X1e or 0x1E (hexadecimal)

= 0b11110 or 0B11110 (binary)



Example:

C:/Ch> int i

C:/Ch> i = 036

30

C:/Ch> i = 0x1e

30

C:/Ch> i = 0b11110

30

C:/Ch> printf(”i = %d\n”, i)

i = 30

C:/Ch> printf(”i = 0%o\n”, i)

i = 036

C:/Ch> printf(”i = 0x%x\n”, i)

i = 0x1e

C:/Ch> printf(”i = 0b%b\n”, i)

i = 0b11110



• Boolean Type

The keyword bool of a declarator in header file stdbool.h can be used to declare variables with boolean data type. For example, the following statement

bool b;

declares a boolean variable b.

A boolean variable only has only two possible values: 1 and 0. Value 1 stands for true and value 0 stands for false. Macro true and false are defined in header file stdbool.h.



• Char Data Representation

– The char data are used to store characters such as letters and punctuation.

An array of char can be used to store a string.

– A character is stored as an integer according to a certain numerical code

such as the ASCII code that ranges from 0 to 127, which only requires 7 bits to

represent it.

– Typically, a char constant or variable occupies 1-byte (8 bits) of unit

memory.

Memory Address Binary value Character

20000 0 1 0 0 1 0 0 0 H

20001 0 1 1 0 0 1 0 1 e

20002 0 1 1 0 1 1 0 0 l

20003 0 1 1 0 1 1 0 0 l

20004 0 1 1 0 1 1 1 1 o

20005 0 0 1 0 0 0 0 1 !



– The macros for minimum and maximum values of signed char are

CHAR_MIN and CHAR_MAX defined in header file limits.h.

CHAR_MIN is equal to -128(-27) and CHAR_MAX is equal to

127(27-1).

– The macro UCHAR_MAX, defined in the header file limits.h,

specifies the maximum value of unsigned short. It is equal to

255(28-1).

• CHAR_MAX = 127 0b0111 1111

• CHAR_MIN = -128 0b1000 0000

• UCHAR_MAX = 255 0b1111 1111



• Character Constants

A character constant, stored as an integer, can be written as one character

within a pair of single quotes like „x‟. A character constant can be

assigned to the variable of type char. For example,

> char c = ‟x‟

> c

x



• Escape Characters Escape Code Description

\a (alert) Produces an audible or visible alert. The active position shall

not be changed.

\b (backspace) Moves the active position to the previous position on the

current line.

\f (form feed) Moves the active position to the initial position at the start

of the next logical page.

\n (new line) Moves the active position to the initial position of the next

line.

\r (carriage return) Moves the active position to the initial position of the

current line.

\t (horizontal tab) Moves the active position to the next horizontal

tabulation position on the current line.

\v (vertical tab) Moves the active position to the initial position of the next

vertical tabulation position.

\\ (backslash) Produces a backslash character \.

\’ (single quote) Produces a single quote character „.

\” (double quote) Produces a double quote character “.

\? (question mark) Produces a question mark character ?.



• String Literals

– A character string literal is a sequence of zero or more multibyte

characters enclosed in double quotes, such as “xyz”.

– Remember that strings represented as character arrays end with

„\0‟.

– Using an array of characters to define a string variable.

> char str1[6] = ”abcde” // The last one is „\0‟

> char str2[] = ”This is a string.”



Arithmetic operations of two

integers are still an integer

> 2+3

5

> 3/2

1

> 2/3

0

> 2.0/3

0.6667



• Floating-Point Types

Floating-point numbers have three representations:

float, double, and long double.

The float data type uses 32 bits (4 bytes) for its storage. The minimum

and maximum values of float data type are defined as macros

FLT_MIN and FLT_MAX, respectively, in header file float.h.

The double data type uses 64 bits(8 bytes) as its storage. The minimum

and maximum values of double data type are defined as macros

DBL_MIN and DBL_MAX, respectively, in header file float.h

The long double should have at least as many bits as double.



Below is a list of metanumbers for floating-point numbers and their

mathematical equivalent.

Metanumbers

Metanumbers Mathematical Representation

-0.0 0-

+0.0 0+

-Inf -

+Inf +

NaN Not-a-Number (Invalid value)



> 0.0/0.0

nan

> 1.0/0.0

inf

> -1.0/0.0

-inf

> sqrt(4)

2.000

> sqrt(-4)

nan

Examples for NaN and Inf



Printing Multiple Numerical Values

in a Single Printing Statement

> printf(”integer is %d, floating-point number is %f”, 10, 12.34)

integer is 10, floating-point number is 12.340000

Use multiple format specifiers.

Each format specifier corresponds to an argument.



Precision of Floating-Point Numbers The precision of a floating-point number specifies the number of digits

after the decimal point character.

The precision typically takes the form of a period (.) followed by

an decimal integer.

For example, the format “%.2f” specifies the precision with 2 digits after

the decimal point.

> printf(”%.2f”, 12.1234)

12.12

> printf(”%.2f”, 12.5678)

12.57

> printf(”%.20f”, 0.2)

0.20000000000000001110

The fractional part after the specified precision number is rounded up.

A floating-point number may not be represented exactly.



Field Width of Numbers The field width is the size of a field in which data are printed.

An integer width is inserted between % and the conversion specifier

to indicate the field width

For example, “%6d” specifies the field width of 6 for an integer,

“8.4” specifies a field width of 8 with 4 digits after the decimal point.

> printf(”%6d”, 12)

12

> printf(”%8.4f”, 5.12345)

5.1234

To print a %, use “%%” in the format string.

> printf(”10%% of 100 is 10\n”)

10% of 100 is 10



• Function scanf() Precise formatting input is accomplished using the input function

scanf. The scanf function has following form

scanf( format-control-string, arguments );

– Format-control-string: Using specifications to describe input

format. Each specification begins with a percent sign(%), ends

with conversion specifier and is enclosed in quotation marks. The

format-control-string is similar to format-control-string discussed

in printf function.

– arguments: pointers to variables in which the input value will be stored.



Table below lists the format-control-string of different argument types for

function scanf(). Using an extra „\n‟ such as “%d\n” is a common mistake.

Argument Type Format-Control-String

char “%c”

short “%hd”

unsigned short “%uhd”

int “%d”

unsigned int “%u”

long long “%lld”

unsigned long long “%ulld”

float “%f”

double “%lf”

string “%s”

pointer “%p”



Example:

> int i

> float f

> double d

> char c

> scanf(“%d”, &i);

10

> i

10

> scanf(“%f”, &f);

10.2

> f

10.20

> scanf(“%lf”, &d);

15

> d

15.0000

> scanf(“%c”, &c);

a

> c

a



Example:

> int i

> scanf(“%d”, &i); // input number in decimal

4261

> Long long l

> scanf(“%lld”, &l); // input into long long number

4261

> l

4261

> scanf(“%b”, &i); // input number in binary in Ch

1000010100101 // or 0b1000010100101

> i

4261

> scanf(“%o”, &i); // input number in octal

10245 // or „010245‟

> i

4261

> scanf(“%x”, &i); // input number in hexadecimal

10A5 // or „0x10A5‟ or „0X10A5‟

> i

4261



/* File: scanfc.c for input and output example */

#include <stdio.h>

int main() {

int num;

double d;

printf("Please input an integer and one floating-point number\n);

scanf("%d%lf",&num, &d);

printf("Your input values are %d and %f\n“, num, d);

return 0;

}

> scanfc.c

Please input one integer and one floating-point number

10 12.3456

Your input number is 10 and 12.345600

>

Program scanf.c

Interactive execution of program scanf.c

Example:

C for Engineers and Scientists: An Interpretive Approach Number Systems …staff.iium.edu.my/farahhani/index_files/ECE 1322_W1_L2_supplemen… · For example, the octal value 45761023

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