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, ...
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Base Two - Binary
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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
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Base Sixteen - Hexadecimal
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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
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.
3a Number Bases
By David James
3a Number Bases
Computer Science - Fundamentals of Data Representation - Number Bases
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