1. Number Systems

2. There are 10 kinds of people in the world, those who understand binary and those who don’t.

3. Quantities/Counting (1 of 3) DecimalBinaryHexadecimal 000 111 2102 3113 41004 51015 61106 71117

4. Quantities/Counting (2 of 3) DecimalBinaryHexadecimal 810008 910019 101010A 111011B 121100C 131101D 141110E 151111F

5. Quantities/Counting (3 of 3) DecimalBinaryHexadecimal 161000010 171000111 181001012 191001113 201010014 211010115 221011016 231011117

6. Conversion Among Bases The possibilities: Hexadecimal Decimal Binary

7. Quick Example 25 10 = 11001 2 = 19 16 Base

8. Binary to Decimal 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

9. Example 101011 2 => 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 = 32 43 10 Bit “ 0 ”

10. 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

11. 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 = 2560 2748 10

12. Exercise 1 Convert (1110101) 2 to decimal Convert (1AF) 16 to decimal

13. 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.

14. Example 125 10 = ? 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1 125 10 = 1111101 2

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

16. Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4

17. Exercise 2 Convert (33) 10 to binary Convert (33) 10 to hexadecimal