1. Hexadecimal
Binary Made Easier

2. Quick Recap Number systems review: System Base Symbols Used by humans?
Used in computers?
Decimal 10
0, 1, … 9
Yes No
Binary 2
0, 1
Sort of

3. Middle Ground Need a system: Easier to read for people
Converts easily to binary

4. Middle Ground Need a system: Hexadecimal – base 16 Easier to read
Converts easily to binary
Hexadecimal – base 16

5. Hexdecimal Base 16 Each column is a power of 16:
= 4096 * * * * 9 =
= 8281 in decimal
4096’s
163
256’s
162
16’s
161
1’s
160 2 5 9

6. 13?
How do we represent 13???
4096’s
163
256’s
162
16’s
161
1’s
160

7. 13?
How do we represent 13???
Use 0-9, A (10), B (11), C (12), D (13), E (14), F (15)
4096’s
163
256’s
162
16’s
161
1’s
160 D

8. 16 Values Each column needs 16 values 0-15
Use 0-9, A (10), B (11), C (12), D (13), E (14), F (15)
= 256 * * * 9 =
= 489
4096’s
163
256’s
162
16’s
161
1’s
160 1 E 9

9. Counting Equivalent values : 1210 = 11002 = C16 1 2 10 3 11 4 100 5
Decimal
Binary
Hex 1 2 10 3 11 4
100 5
101 6
110 7
111
Decimal
Binary
Hex 8
1000 9
1001 10
1010 A 11
1011 B 12
1100 C 13
1101 D 14
1110 E 15
1111 F
Decimal
Binary
Hex 16
10000 10 17
10001 11 18
10010 12 19
10011 13 20
10100 14 21
10101 15 22
10110 23
10111

10. Hex & Binary Each hex digit = 16 possible values
4 binary digits = 16 possible values (24)
1 hex digit = 4 binary digits
Decimal
Binary
Hex 1 2 10 3 11 4
100 5
101 6
110 7
111
Decimal
Binary
Hex 8
1000 9
1001 10
1010 A 11
1011 B 12
1100 C 13
1101 D 14
1110 E 15
1111 F

11. Binary -> Hex
Break binary value into groups of 4:

12. Binary -> Hex Break binary value into groups of 4: 1001110100010110
0000
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
Break binary value into groups of 4:
Replace each group with 1 hex digit

13. Binary -> Hex
Binary
Hex
Decimal
0000
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A 10
1011 B 11
1100 C 12
1101 D 13
1110 E 14
1111 F 15
Break binary value into groups of 4: D
Replace each group with 1 hex digit
= 9D1616

14. Hex -> Binary Replace each hex digit with 4 binary digits: Ex: F2
0000
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
Replace each hex digit with 4 binary digits:
Ex: F2 F
F216 =

15. Hex   Decimal Use a table Digits 0-F 4096’s 256’s 16’s 1’s
A = 10 B = 11 C = 12
D = 13
E = 14
F = 15
4096’s
163
256’s
162
16’s
161
1’s
160

16. Hex   Decimal Use a table Digits 0-F 4096’s 256’s 16’s 1’s 1 C 7
A = 10 B = 11 C = 12
D = 13
E = 14
F = 15
4096’s
163
256’s
162
16’s
161
1’s
160 1 C 7
256 x x x 7 = = 455
1C716 =

17. Decimal   Hex Division / Multiplication methods: ÷ 16 7 12 (C) C7
Current Value
Quotient
Remainder
455
÷ 16 28 7 1
12 (C) C7
1C7

18. Summary Hex is a bridge: Easier for us Still just binary for computers
System
Base
Symbols
Used by humans?
Used in computers?
Decimal 10
0, 1, … 9
Yes No
Binary 2
0, 1
Hex 16
0-9ABCDEF
No, but better than binary
No, but easily translates to binary

19. Colors Monitors make colors by mixing red/green/blue light:
Typical 24 bits : 8 bits for each color
28 = 256 possible values

20. Colors
Hex Colors
Each color stored as 0-255
8 bits
2 hex digits

21. Web Colors Website colors often written in hex #RRGGBB
Two digits for red, two for green, two for blue
Black
#000000
(0,0,0)
White
#FFFFFF
(255,255,255)
Red
#FF0000
(255,0,0)
Lime
#00FF00
(0,255,0)
Blue
#0000FF
(0,0,255)
Yellow
#FFFF00
(255,255,0)
Cyan / Aqua
#00FFFF
(0,255,255)