MicroProcessors Dr. Tamer Samy Gaafar Dept. of Computer & Systems Engineering Faculty of Engineering Zagazig University

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 Grading: Course workGrade distribution Assignments + Sections 12pt 30 Midterm Exam 18pt Final Exam 70pt Total Points100

SystemBaseSymbols Decimal100, 1, … 9 Binary20, 1 Octal80, 1, … 7 Hexa- decimal 160, 1, … 9, A, B, … F BCD (Binary Coded Decimal)  9 in binary representation 0000, 0001,…… 1001

Hexadecimal DecimalOctal Binary

Hexadecimal DecimalOctal Binary

=>5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = Base Weight

Hexadecimal DecimalOctal Binary

 Technique ◦ Multiply each bit by 2 n, where n is the “weight” of the bit ◦ The weight is the position of the bit, starting from 0 on the right ◦ Add the results

 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = Bit “0”

Hexadecimal DecimalOctal Binary

Technique – Multiply each bit by 8 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results

724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 =

Hexadecimal to Decimal Hexadecimal DecimalOctal Binary

Hexadecimal to Decimal Technique – Multiply each bit by 16 n, where n is the “weight” of the bit – The weight is the position of the bit, starting from 0 on the right – Add the results

Example ABC 16 =>C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 =

Decimal to Binary Hexadecimal DecimalOctal Binary

Decimal to Binary Technique – Divide by two, keep track of the remainder – First remainder is bit 0 (LSB, least-significant bit) – Second remainder is bit 1 – Etc.

Example = ? =

Octal to Binary Hexadecimal DecimalOctal Binary

Octal to Binary Technique – Convert each octal digit to a 3-bit equivalent binary representation

Example = ? =

Hexadecimal to Binary Hexadecimal DecimalOctal Binary

Hexadecimal to Binary Technique – Convert each hexadecimal digit to a 4-bit equivalent binary representation

Example 10AF 16 = ? A F AF 16 =

Decimal to Octal Hexadecimal DecimalOctal Binary

Decimal to Octal Technique – Divide by 8 – Keep track of the remainder

Example = ? =

Decimal to Hexadecimal Hexadecimal DecimalOctal Binary

Decimal to Hexadecimal Technique – Divide by 16 – Keep track of the remainder

Example = ? = 4D = D

Binary to Octal Hexadecimal DecimalOctal Binary

Binary to Octal Technique – Group bits in threes, starting on right – Convert to octal digits

Example = ? =

Binary to Hexadecimal Hexadecimal DecimalOctal Binary

Binary to Hexadecimal Technique – Group bits in fours, starting on right – Convert to hexadecimal digits

Example = ? B B = 2BB 16

Octal to Hexadecimal Hexadecimal DecimalOctal Binary

Octal to Hexadecimal Technique – Use binary as an intermediary

Example = ? E = 23E 16

Hexadecimal to Octal Hexadecimal DecimalOctal Binary

Hexadecimal to Octal Technique – Use binary as an intermediary

Example 1F0C 16 = ? 8 1 F 0 C F0C 16 =

Common Powers (1 of 2) Base 10 PowerPrefaceSymbol picop nanon micro  millim 10 3 kilok 10 6 megaM 10 9 gigaG teraT Value

Common Powers (2 of 2) Base 2 PowerPrefaceSymbol 2 10 kilok 2 20 megaM 2 30 GigaG Value What is the value of “k”, “M”, and “G”? In computing, particularly w.r.t. memory, the base-2 interpretation generally applies

Example / 2 30 = In the lab… 1. Double click on My Computer 2. Right click on C: 3. Click on Properties

Review – multiplying powers For common bases, add powers 2 6  2 10 = 2 16 = 65,536 or… 2 6  2 10 = 64  2 10 = 64k a b  a c = a b+c

Binary Addition (1 of 2) Two 1-bit values ABA + B “two”

Binary Addition (2 of 2) Two n-bit values – Add individual bits – Propagate carries – E.g.,

Multiplication (1 of 3) Decimal 35 x

Multiplication (2 of 3) Binary, two 1-bit values AB A  B

Multiplication (3 of 3) Binary, two n-bit values – As with decimal values – E.g., 1110 x

Fractions Decimal to decimal 3.14 =>4 x = x = x 10 0 =

Fractions Binary to decimal => 1 x 2 -4 = x 2 -3 = x 2 -2 = x 2 -1 = x 2 0 = x 2 1 =

Fractions Decimal to binary x x x x x x etc

Exercise – Convert... Don’t use a calculator! DecimalBinaryOctal Hexa- decimal C.82

Exercise – Convert … DecimalBinaryOctal Hexa- decimal …35.63…1D.CC… D C C.82 Answer

DecimalBinaryOctal Hexa- decimal Quantities/Counting (1 of 3)

DecimalBinaryOctal Hexa- decimal A B C D E F Quantities/Counting (2 of 3)

DecimalBinaryOctal Hexa- decimal Quantities/Counting (3 of 3)

The BCD code With this BCD code, each individual digit of the decimal number system is represented by a corresponding binary number So the digits from 0 to 9 can be represented in 4 – bit each (why?)

BCDDecimal Number

The BCD code 4 digits in binary notation are therefore required for each digit in the decimal system Example: Decimal number is thus represented (BCD code)

The BCD code Example: Number in BCD code represents 527 decimal number BCD coded numbers are often used for seven segment displays and coding switches

Thank you