Lecture
- 2. Assessment 2 Total: 100 marks • Final Exam: 60 marks • Mid-term: 15 marks • Oral : 10 marks • Assignments: 10 marks • Participation: 5 marks You will pass if you get 50 marks (PASS)
- 3. Assignments • Google Classroom • Code: 3 x3n5el6
- 4. Numbers 4 • A number is a mathematical object used to count, measure, and label. • Numbers can be represented in languages with symbols. e.g.:
- 5. Digits and Numbers • Digit A digit is a single numerical symbol. For example: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. • Number A number is a string of one or more digits. For example, the number 23 is written with two digits, 2 and 3. 5
- 6. Number Systems 6 System Digits Base Binary 0,1 Base-2 Octal 0,1,2,3,4,5,6,7 Base-8 Decimal 0,1,2,3,4,5,6,7,8,9 Base-10 Hexadecimal 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F Base-16
- 7. Conversion Table 7 Hexadecimal Octal Decimal Binary 0 0 0 0000 1 1 1 0001 2 2 2 0010 3 3 3 0011 4 4 4 0100 5 5 5 0101 6 6 6 0110 7 7 7 0111 8 10 8 1000 9 11 9 1001 A 12 10 1010 B 13 11 1011 C 14 12 1100 D 15 13 1101 E 16 14 1110 F 17 15 1111
- 8. Conversions • Decimal to Other Base System • Other Base System to Decimal • Other Base System to Non-Decimal • Shortcut method − Binary to Octal • Shortcut method − Octal to Binary • Shortcut method − Binary to Hexadecimal • Shortcut method − Hexadecimal to Binary 8 We'll demonstrate here the following:
- 9. Decimal to Other Base System • Step 1 − Divide the decimal number to be converted by the value of the new base. • Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number. • Step 3 − Divide the quotient of the previous divide by the new base. • Step 4 − Record the remainder from Step 3 as the next digit (to the left) of the new base number. Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3. 9 Steps:
- 10. Conversion from decimal to any base (Base-x) 10 ❑ For integer number → divide by x Example: Convert from decimal to binary: (45)10 45 2 22 1 2 11 2 5 2 2 2 1 2 0 0 1 1 0 1 101101 أعلى إلى أسفل من الرقم نكتب (69)10 69 2 34 1 2 17 2 8 2 4 2 2 2 1 0 1 0 0 0 1000101 2 0 1 الباقي
- 11. Conversion from decimal to any base (Base-x) 11 Convert from decimal to octal: 901 901 8 112 5 8 14 0 8 1 6 8 0 1 1605 (901)10 → (1605)8
- 12. Conversion from decimal to any base (Base-x) 12 Convert from decimal to hexadecimal: 1066 1066 16 66 10 16 4 2 16 0 4 (1066)10 → (42A)16
- 13. 13 Conversion from any base (Base-x) to decimal Result = SUM (value * xpos) Example: Convert from binary to decimal: 101011 1 0 1 0 1 1 pos 5 4 3 2 1 0 = 1*20+1*21+0*22+1*23+0*24+1*25 =1+2+0+8+0+32 =43 value (101011)2 → (43)10
- 14. Conversion from any base (Base-x) to decimal 14 Convert from octal to decimal: 672 (672)8=2*80+7*81+6*82 =2+56+384 =(442)10 5061 (5561)8=1*80+6*81+0*82+5*83 =1+48+0+2560 =(2609)10
- 15. Conversion from octal to binary 15 Replace each octal digit into its equivalent 3-bit binary number Convert from octal to binary: (537)8 (537)8= (101 011 111)2
- 16. Conversion from binary to octal 16 كل لّنحو 3bit بال المكافئ الرقم الى octal Convert from binary to octal: a) 111110110 (111 110 110)2=(766)8 b) 1000001 (001 000 001)2=(101)8 الصحيح العدد في بنبدأ الشمال على أصفار نزود وممكن اليمين من علشان نكمل 3 bit
- 17. Conversion from hexadecimal to binary 17 Replace each hexadecimal digit into its equivalent 4-bit binary number Convert from hexadecimal to binary: (A8C3)16 (A8C3)16= (1010 1000 1100 0011)2
- 18. 18 Conversion from binary to hexadecimal كل لّنحو 4bit بال المكافئ الرقم الى hexadecimal الصحيح العدد في بنبدأ الشمال على أصفار نزود وممكن اليمين من علشان نكمل 4 bit Convert from binary to hexadecimal: a) 10101001 (1010 1001)2= (A9)16 d) 01101111 (0110 1111)2= (6F)16
- 19. Conversion from octal to hexadecimal 19 Octal → Binary → Hexadecimal Convert from octal to hexadecimal: A) 777 (777)8 → (111111111)2 → (0001 1111 1111)2 → (1FF)16 B) 605 (605)8 → (110000101)2 → (0001 1000 0101)2 → (185)16 C) 443 (443)8 → (100100011)2 → (0001 0010 0011)2 → (123)16
- 20. 20 Conversion from hexadecimal to octal Hexadecimal → Binary → Octal Convert from hexadecimal to octal: A) A9 (A9)16=(10101001)2=(010 101 001)2=(251)8 B) E7 (E7)16=(11100111)2=(011 100 111)2=(347)8
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