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Logic Design (CE1111 ) Lecture 1.2 (Chapter 1) Prepared by Dr. Lamiaa Elshenawy 1.

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Presentation on theme: "Logic Design (CE1111 ) Lecture 1.2 (Chapter 1) Prepared by Dr. Lamiaa Elshenawy 1."— Presentation transcript:

1 Logic Design (CE1111 ) Lecture 1.2 (Chapter 1) Prepared by Dr. Lamiaa Elshenawy 1

2 Outlines  Digital Systems  Binary Numbers  Number-Base Conversions  Octal and Hexadecimal Numbers  Complements of Numbers  Signed Binary Numbers  Binary Codes  Binary Storage and Registers  Binary Logic 2

3 Complements of Numbers  Complements are used in digital computers to simplify the subtraction operation and for logical manipulation  Simplifying operations leads to simpler, less expensive circuits to implement the operations 3

4 Complements of Numbers  Types of complements 1. Radix complement (r’s complement) 2. Diminished radix complement ((r-1)’s complement)  Decimal Numbers O 10’s complement and 9’s complement  Binary Numbers O 2’s complement and 1’s complement 4

5 Complements of Numbers 5

6  Calculate the 10’s complement and 9’s complement of 546700.  Solution  10’s complement: 1000000 - 546700=453300  9’s complement: 999999 - 546700=453299 6

7 Complements of Numbers  Calculate the 2’s complement and 1’s complement of 1011000.  Hint  Solution  2’s complement: 1011000 0101000  1’s complement: 1011000 0100111 7  2’s complement: leave all least significant 0’s and first 1 unchanged, change from 0 to 1 or from 1 to 0 for all other higher significant digits  1’s complement: change from 0 to 1 or from 1 to 0

8 Signed Binary Numbers  Leftmost position of the number used for sign: O Bit 0 Positive number O Bit 1 Negative number  Example  (+9) 10 =(01001) signed-magnitude representation  (-9) 10 =(11001) 2 signed-magnitude representation  (-9) 10 =(10110) 2 signed-1’s complement representation  (-9) 10 =(10111) 2 signed-2’s complement representation 8

9 9

10 Arithmetic Addition 10

11 Arithmetic Addition  Example 11

12 Arithmetic Subtraction 12

13 Arithmetic Subtraction 13 Discard

14 Binary Codes 14

15 Binary Codes  What are the most common binary codes? 1. Binary-Coded Decimal (BCD) 2. 2421-Code 3. Excess-3 Code 4. 8,4,-2,-1 Code 5. Gray Code 6. ASCII Character Code 15

16 Binary-Coded Decimal  Converts Decimal Numbers Binary Numbers  How?  Write each decimal digits in 4bits  Example 16

17 Binary-Coded Decimal 17

18 Signed-BCD Addition 18

19 19

20 20

21 ASCII Character Code  It codes 128 Characters in7-bits 1. 26 capital letters 2. 26 small letters 3. 10 decimal digits 4. Special characters 21 ASCII: American Standard Code for Information Interchange

22 22

23 23

24 Registers  What is a register?  A register is a group of binary cells. A register with n cells can store any discrete quantity of information that contains n bits 24

25 25 Register Transfer

26 26 Information Processing

27 Binary Logic  What is a binary logic?  Binary logic consists of binary variables and a set of logical operations  Variables are designated by letters of the alphabet, such as A, B, C, x, y, z, etc., with each variable having two and only two distinct possible values: 1 and 0 27

28 Binary Logic 28

29 Binary Logic 29

30 30


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