Introduction to Microprocessors Chapter 2

Decimal or Base 10 Numbers  Have ten different digits (0-9)  It is a weighted number system. Each position as you move to the left has a weight of the base (10 for decimal) raised to an integer power. The first position (from right to left) has power of zero, next position power of one…….  Ex: 123 = (1 x 10 2 ) + (2 x 10 1 ) + (3 x 10 0 )

Binary numbers  They have two digits (0 & 1)  To convert it to decimal:  ex1: = (1 x 2 2 ) + (0 x 2 1 ) + (1 x 2 0 ) = = 5 10  ex2: = (1 x 2 3 ) + (1 x 2 2 ) + (0 x 2 1 ) + (0 x 2 0 ) = =12 10  ex3: = (1 x 2 4 ) + (1 x 2 3 ) + (0 x 2 2 ) +  (0 x 2 1 ) + (1 x 2 0 ) = =25 10

Convert Decimal to Binary  Repeated division by 2  Ex: = ? 2  18/2=9 and reminder is 0  9/2 = 4 and reminder is 1  4/2 =2 and reminder is 0  2/2 =1 and reminder is 0  ½ = 0 and reminder is 1  Therefore =

Hexadecimal (base 16)  Need 16 digits.  We use our ordinary decimal digits (0-9) and A-F

Hex to decimal ex1: = (1 x 16 2 ) + (2 x 16 1 ) + (3 x 16 0 ) = = ex2: 1A 16 = (1 x 16 1 ) + (10 x 16 0 ) = =26 10

Decimal to Hex Repeated division by 16 Ex1: = ? 16 26/16=1 and reminder is 10 (A) 1/16 = 0 and reminder is 1 Therefore = 1A 16 Ex2: = 53 16

Determine next number in HEX  2E  9F  7CBF

Hex to Binary  Convert each digit to 4 bits binary equivalent  Example: AB35H

Binary to Hex  Break binary number into 4-bit sections from LSB to MSB  Convert the 4 bits binary to its hex equivalent  Example:  Add zeros to the left if necessary A F B 2

Two’s complement signed number  Positive number ex: =  Negative number is shown as 2’s complement of positive number  Write number as 8 bits  Complement each bit (0 ->1 and 1-> 0)  Add 1  Ex: = ?  (1’s complement) =>  1 

Signed & unsigned numbers  8 bit unsigned can represent 0 to  8 bit signed can represent -128 to  2’s complement of a negative number is it’s corresponding positive number.  We do not have negative & positive zero!  If you have a negative number, How do you get its decimal equivalent??

2’s complement application  CPU do not need 2 separate hardware module to perform add & subtraction. Subtraction can be done as: a – b = a + (-b)

ASCII Code  American Standard Code for Information Interchange  7 bits needed. Ex: code for Q is 51( )  One bit is added for Parity  Parity is even or odd  Even parity: Number of 1s are even ex:  Odd parity: Number of 1s are odd

Binary Coded Decimal (BCD)  Each decimal digit is represented by 4 bits  Example1: 53  Example 2:

Application of BCD  Most common application of BCD is with seven-segment displays  BCD to seven segment decoder inputs one 4- bit BCD and outputs a segment pattern-code

Seven-segment  The display consists of seven individual bar LEDs  Displays decimal and hexadecimal values  The LED segments are labeled “a” through “g”  To illuminate a “0” on the display, segment “a” through “f” are illuminated

Overflow  Whenever two signed numbers are added or subtracted and the result is too large for the number of bits allocated

No overflow when adding a positive and a negative number No overflow when subtracting numbers with the same sign Overflow occurs when the result has “wrong” sign (verify!): Operation Operand A Operand B Result Indicating Overflow A + B  0  0  0 A + B  0  0  0 A – B  0  0  0 A – B  0  0  0 Detecting Overflow

Computer Programming  High level language  Assembly Language  Machine Language