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 87C987C9 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 6A8. F 5 C

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

6. Hex Octal Go through Binary 0110 1010 1000. 1111 0101 1100 6A8. F 5 C 011 010 101 000. 111 101 011 100 3 2 5 0. 7 5 3 4

7. Convert Decimal to any Base Integer Part: Divide by the base, keep track of the remainder, and read up. 16 34,761 16 2,172rem 9 16 135 rem 12 = C 16 8 rem 7 0 rem 8 Read up 34,761 10 = 87C9 16

8. 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 Read down 0.78125 10 = C8 16

9. 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 Read down 0.1 10 = 0.00011 2

10. Questions 10010101 2 = ? (decimal)

11. Questions 857 10 = ? 16

12. Questions BED 16 = ? 2