16-bit Memory Word CSCI 125 & 161 / ENGR 144 To store number - - PDF document

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16-bit Memory Word CSCI 125 & 161 / ENGR 144 To store number 6, use 0000000000000110 Lecture 5 Value 0 is 0000000000000000 Martin van Bommel Largest value is 1111111111111111 = 65,535 = 2 16 1 32-bit word gives

SLIDE 1

1 CSCI 125 & 161 / ENGR 144 Lecture 5

Martin van Bommel

16-bit Memory Word

To store number 6, use 0000000000000110
Value 0 is 0000000000000000
Largest value is

1111111111111111 = 65,535 = 216 − 1

32-bit word gives largest value > 4 billion

Storing Negative Values

Sign Magnitude

– use first bit as sign bit, 0 = positive 1 = negative – e.g. 8-bits 00000000 = 0 10000000 = −0 00000001 = 1 10000001 = −1 … … 01111111 = 127 11111111 = −127

Two’s Complement

Two’s complement

– if positive, use binary – if negative, complement bits and add one – e.g. −53 magnitude 00110101 complement 11001010 add 1 11001011

8-bit Two’s Complement

00000000 = 0 00000001 = 1 11111111 = −1 00000010 = 2 11111110 = −2 … … 01111111 = 127 10000001 = −127 10000000 = −128

Two’s Complement Addition

Add −1 + 2?

−1 11111111 +2 00000010

00000001

SLIDE 2

2 16-bit Two’s Complement

8-bit two’s complement range is

− 27 = − 128 to 27 − 1 = 127

16-bit two’s complement range is

− 215 = −32,768 to 215 − 1 = 32,767

32-bit two’s complement range is

− 231 −2 million to 231 − 1 2 million

Data Types

Two properties

– set of values (domain) – set of operations

int - 32-bit two’s complement integers
2 147 483 648 to 2 147 483 647

+, -, *, /, %

Floating-point Data

Numbers that include fractional parts
float - 32-bit floating point representation

– approximately seven decimal digits of accuracy

double - 64-bit floating point representation

– approximately sixteen decimal digits of accuracy

+, -, *, /

Character Data

char - Elements from the ASCII table
Values expressed in single quotes

e.g. ’A’ ’?’ ’\n’

stored in memory as their ASCII value

+, -

Expressions

A sequence of terms and operators
Term - represents single data value

– constant - data value as part of program, e.g. 4 – variable - name as placeholder for memory – function call - one that generates a value

e.g. sqrt(9)

– expression in parenthesis

Operator - character indicating computation

Constants

Explicit values that never change
Integer constants - sequence of digits

– e.g. 1000; 5; 1 not 1,000; 3.14

Floating-point constant - includes decimal

– e.g. 3.14; 1.0; 2.9E+8

String constant - characters in double quotes

– e.g. “Hello, world.\n”

SLIDE 3

3 Variables

Placeholder for value in memory

– name - alias for memory location – value - current value stored in location – type - kind of data values that may be stored

name value

Variable Names

Must start with letter or underscore ( _ )

followed by letters, digits, or underscores

Case of letters significant
Name not a C++ keyword
Name any length, but only 31 characters

significant (safe only up to 8 characters)

Operators and Operands

expression operator expression
e.g. (2 * x) + (3 * y)
expressions are operands - values to which
perator is applied
operator signifies operation
binary operators - two operands e.g. a + b
unary operators - one operand e.g. - b

Combining Integers and Floats

Result of expression is most specific type
e.g. Value of 2.5 + 3 is 5.5
type of expression n + 1 is type of n
type of expression n + 1.5 is float if

n is float or int, but double if n is double

Integer Division and Remainder

Division of int’s results in int
Remainder operator % gives remainder
e.g. 5 / 2 is 2

5 % 2 is 1

5 / 2.0 is 2.5

0 % 4 is 0

5.0 / 2 is 2.5

1 % 4 is 1

5.0 / 2.0 is 2.5

4 % 4 is 0

Precedence Rules

Parenthesized expressions first
Unary minus operator next
*, /, and % next, from left to right
+ and - next, from left to right
e.g.

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CSCI 125 & 161 / ENGR 144 Lecture 5