1. Eng. Mohammed Timraz Electronics & Communication Engineer University of Palestine Faculty of Engineering and Urban planning Software Engineering Department Digital Logic Design Lab. ESGD2101 Wednesday, 30 th January 2008 Lab. 1 Number Systems

2. 1- Decimal Number: [Base10], * Integer Number:[0,1,2,3,………..9] Example:- [23] 10 =3×10 0 +2 × 10 1 =3 × 1+2 × 10 =3+20= 23 Number Systems

3. Decimal Number *Float Number: [16. 15] Integer partfloat part Decimal Point Example:- [16.15] 16.15=6*10 0 +1*10 1 +1*10 -1 +5*10 -2 =6 + 10 + 0.1 + 0.05 =16.15 …..10 4 10 3 10 2 10 1. 10 -1 10 -2 10 -3 10 -4 …..Decimal Point Number Systems

4. 2. Binary Numbers: [Base 2],[ 0,1] ex:- 00,01,10,11 Decimal Binary Number Systems 000 101 210 311

5. 2-1 Binary to Decimal Conversion: Example:- [1101101] 2 1101101 MSBLSB Most significant BIT Least Significant Bit Number Systems

6. 2-1 Binary to Decimal Conversion: Example:- For integer numbers, [1101101] 2 = [ ? ] 10 1101101 2 6 2 5 2 4 2 3 2 2 2 1 2 0 [1101101] 2 =1×2 0 +0×2 1 +1×2 2 +1×2 3 +0×2 4 +1×2 5 +1×2 6 =[109] 10 MSBLSB

7. Number Systems 2-1 Binary to Decimal Conversion: Example:- For float numbers, [10.111] 2 = [ ? ] 10 10.111 2 1 2 0 2 -1 2 -2 2 -3 [10.111] 2 =0×2 0 +1×2 1 +1×2 -1 +1×2 -2 +1×2 -3 =[2.875] 10 Note: MSB & LSB just for integer part. Binary point

8. Number Systems 2-1 Binary to Decimal Conversion: Example:- [1011] 2 = [ ? ] 10 1011 2 3 2 2 2 1 2 0 [1011] 2 =1×2 0 +1×2 1 +0×2 2 +1×2 3 =[11] 10

9. Number Systems 2-2 Decimal to Binary Conversion: There are two ways to convert the decimal numbers to binary numbers. 1.By using the Truth Table: we can use the truth table for small decimal numbers, but for large decimal numbers it will be more difficult. 2.So, we will use the division: which we can use it for small and large decimal numbers

10. Binary 2 3 2 2 2 1 2 0 Decimal 0 0 0 0 0 0 11 0 0 1 02 0 0 1 13 0 1 0 04 0 1 5 0 1 1 06 0 1 1 17 1 0 0 08 1 0 0 19 1 0 1 0 1 111 1 1 0 012 1 1 0 113 1 1 1 014 1 1 15 Number Systems The Truth Table Decimal to Binary Conversion:

11. Number Systems Decimal to Binary Conversion: The Division: [198] 10 = [ ? ] 2 By using the division system: 0 1 1 0 0 0 1 1 011 00011 Carrier

12. 3. Octal Numbers: [Base 8],[ 0,1,3,4,5,6,7] Number Systems 3-1 Octal to Decimal Conversion: Example:- [2374] 8 = [ ? ] 10 =4×8 0 +7×8 1 +3×8 2 +2×8 3 =[1276] 10

13. Number Systems 3-2 Decimal to Octal Conversion: The Division: [359] 10 = [ ? ] 8 By using the division system: 7 4 5 74 5 Carrier

14. Number Systems 3-3 Binary to Octal Conversion: Example:- [110101] 2 = [ ? ] 8 Here we will take 3 bits and convert it from binary to decimal by using the decimal to binary truth table: BinaryDecimal 1106 1015 1 1 01 0 1= (65) 8 {{ 65

15. Number Systems 3-4 Octal to Binary Conversion: Example:- [13] 8 = [ ? ] 2 Here we will convert each decimal digit from decimal to binary (3 bits) using the decimal to binary truth table: BinaryDecimal 1001 3011 (13) 8 = (001011) 2

16. 4. Hexa Decimal Numbers: [Base 16],[ 0,1,3,4,5,6,7,8,9,A,B,C,D,E,F] Number Systems 4-1 Binary to Hexa Decimal Conversion: Example:- [1100101001010111] 2 = [ ? ] 16 Here we will take 4 bits and convert it from binary to decimal by using the decimal to binary truth table: 1100101001010111 {{{{ CA75 Then, [1100101001010111] 2 = [CA57] 16

17. Number Systems 4-2 Hexa Decimal to Binary Conversion: Example:- [DE27] 16 = [ ? ] 2 Here we will convert each Hexa decimal digit from decimal to binary (4 bits) using the decimal to binary truth table: DE72 Then, [DE27] 16 = [1101111000100111] 2 1101111000100111

18. Number Systems 4-3 Hexa Decimal to Decimal Conversion: Example:- [B2F8] 16 = [ ? ] 10 =8×16 0 +F×16 1 +2×16 2 +B×16 3 =[45816] 10 Where, B=11, and F=15

19. Number Systems 4-4 Decimal to Hexa Decimal Conversion: Example:- [650] 10 = [ ? ] 16 By using the division system: 10 8 2 Carrier A8 2