CSCI 125 & 161 / ENGR 144 Lecture 5

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 ---- ------------ +1 00000001

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”

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 operator 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. 8 * (7 - 6 + 5) % (4 + 3 / 2) - 1

CSCI 125 & 161 / ENGR 144 Lecture 5