3a Number Bases
- Understand the following number bases: decimal (base 10), binary (base 2), hexadecimal (base 16).
- Understand that computers use binary to represent all data and instructions.
- Explain why hexadecimal is often used in computer science.
Base Ten - Denary or Decimal
- Ten digits (fingers)
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
- After nine, move left a place:
- 10, 11, 12, ...
- After ninety-nine, move left a place:
- 100, 101, ...
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, FA = 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, 0F10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F20, 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, EFF0, 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
12110
011110012
7916
Denary
Binary
Hexadecimal
Number Bases Assessment
- Why do humans use denary?
- What do computers use for all data?
- Why is hexadecimal used?
- How many binary bits does one hexadecimal digit replace?
3a Number Bases Understand the following number bases: decimal (base 10), binary (base 2), hexadecimal (base 16). Understand that computers use binary to represent all data and instructions. Explain why hexadecimal is often used in computer science.