CCE Department – Faculty of engineering - Islamic University of Lebanon Chapter 6 Binary Arithmetic

CCE Department – Faculty of engineering - Islamic University of Lebanon Addition 1

CCE Department – Faculty of engineering - Islamic University of Lebanon Binary Addition Binary addition is very simple. This is best shown in an example of adding two binary numbers… carries

CCE Department – Faculty of engineering - Islamic University of Lebanon Binary addition example worked out Some terms are given here Exercise: what are these numbers equivalent to in decimal? (Carries) 1011(Augend) +1110(Addend) 11001(Sum) The initial carry in is implicitly 0 most significant bit (MSB) least significant bit (LSB)

CCE Department – Faculty of engineering - Islamic University of Lebanon Subtraction 4

CCE Department – Faculty of engineering - Islamic University of Lebanon Binary Subtraction 5 °We can also perform subtraction (with borrows in place of carries). °Let’s subtract (10111) 2 from ( ) 2 … borrows

CCE Department – Faculty of engineering - Islamic University of Lebanon Negative Numbers 6 Subtract by adding ’s complement Ignore carry

CCE Department – Faculty of engineering - Islamic University of Lebanon Two’s Complement Shortcuts Algorithm – Simply complement each bit and then add 1 to the result. –Finding the 2’s complement of ( ) 2 and of its 2’s complement… N = [N] =

CCE Department – Faculty of engineering - Islamic University of Lebanon Negative Numbers 8 Subtract by adding ’s comp flip

CCE Department – Faculty of engineering - Islamic University of Lebanon 9

Signed Numbers 10 4-bit: 8H = -8 to 7H = to bit: 80H = -128 to 7F = bit: 8000H = -32,768 to 7FFFH = +32, bit: H = -2,147,483,648 to 7FFFFFFFH = +2,147,483,647

CCE Department – Faculty of engineering - Islamic University of Lebanon Questions 11 What is the two’s complement of ? What hex number represents the decimal number -40?

CCE Department – Faculty of engineering - Islamic University of Lebanon Multiplication 12

CCE Department – Faculty of engineering - Islamic University of Lebanon Binary Multiplication Binary multiplication is much the same as decimal multiplication, except that the multiplication operations are much simpler… X

CCE Department – Faculty of engineering - Islamic University of Lebanon ASCII CODES 14

CCE Department – Faculty of engineering - Islamic University of Lebanon ASCII The most commonly used code for representing letters, numerals and punctuation characters (alphanumeric data) Each character is represented with a 7-bit string; for example: ‘3’ = (hex 33) ‘ ’ = (hex 20) An 8-bit extension of ASCII has also been defined 15

CCE Department – Faculty of engineering - Islamic University of Lebanon ASCII Code American Standard Code for Information Interchange ASCII is a 7-bit code, frequently used with an 8 th bit for error detection (more about that in a bit). 16 CharacterASCII (bin) ASCII (hex) Decimal A B C … Z a … 1 ‘

CCE Department – Faculty of engineering - Islamic University of Lebanon ASCII Properties 17 Q1: What is relationship between a decimal digit (0, 1, …) and its ASCII code?

CCE Department – Faculty of engineering - Islamic University of Lebanon ASCII Properties (2) 18 Q2: What is the difference between an upper-case letter (A, B, …) and its lower-case equivalent (a, b, …)?

CCE Department – Faculty of engineering - Islamic University of Lebanon BCD 19

CCE Department – Faculty of engineering - Islamic University of Lebanon Binary Coded Decimal Binary coded decimal (BCD) represents each decimal digit with four bits –Ex = 329 BCD This is NOT the same as Why do this? Because people think in decimal. 20 DigitBCD CodeDigitBCD Code

CCE Department – Faculty of engineering - Islamic University of Lebanon Putting It All Together 21 °BCD not very efficient °Used in early computers (40s, 50s) °Used to encode numbers for seven- segment displays. °Easier to read?