3.1-3.2 Numbers and characters coding systems

1. 3.1-3.2Numbers and characters coding systems Tsang Tin Chuen 4E(17)

2. 3.1 Denary, Binary and Hexadecimal Number Systems • We often use denary system (base 10) 210, 9910, 123410 Computer systems operates with binary systems (base 2) Hexadecimal systems (base 16) is also used for us (human) to read more easily.

3. What are binary number system? • A method of representing numbers in which only the digits 0 and 1 are used. Like 11012 101111010101110102 Therefore, successive units are powers of 2.

4. It means……… “2, 3…..” will not be used • 17X When the digit reaches 2, the next digit is used instead. 2 102

5. Examples: Binary digit Place value Digit Value

6. In the other way round…. • Hexadecimal Number Systems is a method of representing numbers in which the digits from 0 to 9 plus letters from A to F are used. • Therefore, successive units are powers of 16

7. Remarks When the digits reach 10, A is used instead….. Base 10 Base 16

8. Example • Binary digit • Place value • Digit Value

9. 3.2 conversion Binary  Denary Method: Just expand it. (add all the digits values)

10. Binary  Denary 11012 =1x23 +1x22 + 0x 21+1x 20 = 8+4+0+1 =1310

11. Denary  Binary Method: Divide the number by 2 until quotient < 2 2 │31 …1 │15 … 1 Obtain the answer by │7 ... 1 Writing up from the quotient │3 …1 to the remainder 1 in reverse order 312 = 111112

12. Binary  Hexadecimal Grouping Method: Since 24=16, we can put 4 digits in a group. This makes both are from 0-15. e.g 111111011000002 11 111101100000 = (2 15 6 0 ) = 2F6016

13. Hexadecimal  Binary By a similar way…. 4D9B16 =4 13 9 11 = 100 1101 1001 1011 =1001101100110112

15. ThE EnD