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Computer Science IGCSEPDF 6
142 pagesrevision 46930
PDF 6
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Example: 10110₂ = (1×16)+(0×8)+(1×4)+(1×2)+(0×1) = 22
₁₀
Denary to Binary Conversion
Method 1: Repeated Division by 2 → 22 = 10110₂
Method 2: Subtracting Powers of 2 → 22 = 10110₂
Binary Arithmetic
0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1)
Example: 1011 + 0111 = 10010₂
Signed Binary (Two’s Complement)
Used to represent negative numbers.
Steps: Write positive number → Invert bits → Add 1.
Example: -5 in 8 bits → 00000101 → 11111010 + 1 → 11111011
1.2 Hexadecimal Systems
The hexadecimal system is base-16, using digits 0–9 and A–F. Each hex digit equals 4 binary
digits (a nibble).
Example: A3₁₆ = 10100011₂ | 1101001101₂ = 34D₁₆
Uses:
-HTML colour codes (#FF5733)
-MAC addresses
-Memory addressing in programming
1.3 Character Sets & File Sizes
Computers store text using character codes that map symbols to numbers.