Base Two - Binary

Base Two - Binary

• Two digits (TRUE/FALSE, on/off)
• 0, 1
• After one, move left a place:
  • 10, 11
• After three (11 in binary), move left a place:
  • 100, 101, ...

Base Two - Binary

• Binary is the language of computers
• All data processed by a computer is in binary
• Very difficult for humans to read and write in binary

Base Sixteen - Hexadecimal

Base Sixteen - Hexadecimal

• Sixteen digits (represents 4 bits)

• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

• A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

• Usually written as a pair of digits:

• 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0A, 0B, 0C, 0D, 0E, 0F

• After fifteen, move left a place, etc...

  • 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 0A, 0B, 0C, 0D, 0E, 0F

  • 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F

  • 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2A, 2B, 2C, 2D, 2E, 2F

  • ...

  • E0, E1, E2, E3, E4, E5, E6, E7, E8, E9, EA, EB, EC, ED, EE, EF

  • F0, F1, F2, F3, F4, F5, F6, F7, F8, F9, FA, FB, FC, FD, FE, FF

Base Sixteen - Hexadecimal

• Hexadecimal is a stepping stone to binary for humans
• Easy to convert to and from binary
• Much shorter to write
• Easier to read

Number Bases Assessment

1. Why do humans use denary?
2. What do computers use for all data?
3. Why is hexadecimal used?
4. How many binary bits does one hexadecimal digit replace?

Number Bases Answers

1. Why do humans use denary?
   They have ten fingers (digits)
2. What do computers use for all data?
   Binary
3. Why is hexadecimal used?
   It is easier for humans to use than binary
4. How many binary bits does one hexadecimal digit replace?
   4 bits (F16 = 11112 = 1510)