1. NUMBER SYSTEMS Binary Base 2 Octal Base 8 DecimalBase 10 HexadecimalBase 16

2. DECIMAL Normally, we count things in base 10. The base is completely arbitrary. The only reason that people have traditionally used base 10 is that they have 10 fingers, which have made handy counting tools. 0 1 2 3 4 5 6 7 8 9 (Total 10) Wonder if we had only 2 fingers?  BASE-10

3. DECIMAL NUMBER MEANS The number 532.25 in decimal (base 10) means the following: = (5 * 10 2 ) + (3 * 10 1 ) + (2 * 10 0 ) + (2 * 10 -1 ) + (5 * 10 -2 ) = 500 + 30 + 2 + 2/10 + 5/100 = 532.25

4. BINARY TO DECIMAL In the binary number system (base 2), each column represents a power of 2 instead of 10. For example, the number 101.01 means the following: = (1 * 2^2) + (0 * 2^1) + (1 * 2^0) + (0 * 2^-1) + (1 * 2^-2) 4 + 0 + 1 + 0 + 1/4 = 5.25 Decimal 4 + 0 + 1 + 0 + 1/4 = 5.25 Decimal For simplicity we are NOT going to discuss Fractions

5. HEXADECIMAL TO DECIMAL FF F in Hex is 15 so =15 x 16 1 + 15 x 16 0 = 240 + 15 = 255 Check it ! = 255 Check it ! 0 1 2 3 4 5 6 7 8 9 a b c d e f HEXADECIMAL NUMBERS!

7. OCTAL TO DECIMAL e.g 56564OCT is Base 8 = 5 x 8 4 + 6 x 8 3 + 5 x 8 2 + 6 x 8 1 + 4 x 8 0 = 5 x 4096 + 6 x 512 + 5 x 64 + 6 x 8 + 4 x 1 = 20480 + 3072 + 320 + 48 + 4= 23924

8. DECIMAL TO BINARY 2100 250 – 0 225 – 0 212 – 1 26 – 0 23 – 0 1 - 1 Answer: 1100100

9. DECIMAL TO HEXADECIMAL 16100 6 - 4 16222 13(D) – 14 (E) 161000 1662 – 8 3 - 14 Convert all above 9 to A B C etc 3 14 8 3 E 8

10. DECIMAL TO OCTAL 864 88 - 0 1 – 0 So answer is 100 Octal equals 64 DECIMAL

11. BINARY TO OCTAL OKAY! Lets keep it very simple –Convert Binary to Decimal –And the Decimal to Octal