Number System Conversions

1. Number System Conversions Lecture L2.2 Section 2.3

2. Number System Conversions • Hex, Binary, and Octal to Decimal • Binary Hex • Binary Octal • Hex Octal • Decimal to Hex, Octal, and Binary

3. Hex to Decimal 8 7 C 9 x 16 128 + 7 135 x 16 2,160 + 12 2,172 x 16 34,752 + 9 34,761

4. Binary Hex 0110 1010 1000 . 1111 0101 1100 6 A 8 . F 5 C

5. Binary Octal 011 010 101 000 . 111 101 011 100 3 2 5 0 . 7 5 3 4

6. Hex OctalGo through Binary 0110 1010 1000 . 1111 0101 1100 6 A 8 . F 5 C 011 010 101 000 . 111 101 011 100 3 2 5 0 . 7 5 3 4

7. Read up Convert Decimal to any Base Integer Part: Divide by the base, keep track of the remainder, and read up. 16 34,761 16 2,172 rem 9 16 135 rem 12 = C 16 8 rem 7 0 rem 8 34,76110 = 87C916

8. Read down Convert Decimal to any Base Fractional Part: Multiply by the base, keep track of the integer part, and read down. 0.78125 x 16 = 12.5 int = 12 = C 0.5 x 16 = 8.0 int = 8 0.7812510 = C816

9. Read down Convert Decimal to any Base Fractional Part: Multiply by the base, keep track of the integer part, and read down. 0.1 x 2 = 0.2 int = 0 0.2 x 2 = 0.4 int = 0 0.4 x 2 = 0.8 int = 0 0.8 x 2 = 1.6 int = 1 0.6 x 2 = 1.2 int = 1 0.2 x 2 = 0.4 int = 0 0.4 x 2 = 0.8 int = 0 0.110 = 0.000112

10. Questions 10010101 = ? (decimal) 2

11. Questions 85710 = ?16

12. Questions BED = ? 16 2