1. Hexadecimal numbers

2. Announcements Meeting of the Mathematics and Computing Society, Thursday 12:30pm BSC 126 Help available in Math Lab Check homework due in assignment schedule

3. Why Hexadecimal numbers? Binary numbers are long and difficult to read. Hexadecimal numbers are efficient to use for the computers and easy to read to human.

4. What are hexadecimal numbers?

5. Convert to decimal 161 1 3D = 13

6. Convert to decimal 16 2 16116 2 161 A = 105F = 15

7. Convert Hexadecimal to binary Method works only for hexadecimal not for decimal B32 16 7931 16 Convert the decimal number 229 to decimal

8. Hexadecimal to binary Hexadecimal Digit Binary Number 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001 A1010 B1011 C1100 D1101 E1110 F1111 B32 16 B1011 B32 16 = 1011 0011 0010 2 B1011 30011 20010 B1011 30011

9. Hexadecimal to binary Hexadecimal Digit Binary Number 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001 A1010 B1011 C1100 D1101 E1110 F1111 7931 16 70111 7951 16 = 0111 1001 0011 0001 2 70111 91001 30011 70111 91001 30011 10001 70111 91001

10. From Decimal to Binary We need to use repeated subtraction Greatest power of two that fits into 229  128 229 -128 = 101  next power of twos: 64 101 – 64 = 37  next power of twos: 32 37 – 32 = 5  next power of twos: 4 5 – 4 = 1  next power of twos: 1 1 – 1 = 0 Stop 1286432168421 1 1286432168421 11 1286432168421 111 1286432168421 1111 1286432168421 11111 1286432168421 11100101 229 = 1110 0101 2

11. From Binary to Hexadecimal 1101 1001 1101 1001= D9 16 Hexadecimal Digit Binary Number 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001 A1010 B1011 C1100 D1101 E1110 F1111 1101 D D 1001 9

12. From Binary to Hexadecimal 11110011001 2 Rewrite in packets of 4, starting from right: 111 1001 1001 2 Add 0 to left to complete packets of 4: 0111 1001 1001 2 Proceed as in previous slide

13. From Binary to Hexadecimal 0111 1001 1001 2 0111 1001 1001= 799 16 Hexadecimal Digit Binary Number 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001 A1010 B1011 C1100 D1101 E1110 F1111 0111 7 7 1001 9 0111 7 1001 9 9

14. Practice Hexadecimal to decimal: 2B 16, 5F6 16 Hexadecimal to binary: A4C 16, 718 16 Decimal to binary: 218 Binary to Hexadecimal: – 1011 1101 0101 – 1110011101 Binary to decimal: – 1011 1101