LESSON 4: NUMBER SYSTEMS

Base-N Number System

• N Digits: 1, 2, 3, 4, ..., N-1

• Example: 1045_N

  • d₀: least significant digit (LSD)

  • dₙ₋₁: most significant digit (MSD)

Decimal Number System

• Base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

• Example: 1045₁₀

  • d₀: least significant digit (LSD)

  • dₙ₋₁: most significant digit (MSD)

Binary Number System

• Base 2: 0, 1

• Example: 1010110₂

• Bits:

  • b₀: least significant digit (LSD)

  • bₙ₋₁: most significant digit (MSD)

• Data Sizes:

  • Nybble = 4 bits

  • Byte = 8 bits

  • Short word = 2 bytes = 16 bits

  • Double word = 4 bytes = 32 bits

  • Long word = 8 bytes = 64 bits

• Units:

  • 1K (kilo or “kibi”) = 1,024

  • 1M (mega or “mebi”) = (1K)² = 1,048,576

  • 1G (giga or “gibi”) = (1K) (1M) = 1,073,741,824

Hexadecimal Number System

• Base 16: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

• Example: EF56₁₆

Binary Representation of Hexadecimal Digits

Binary Addition

Single Bit

• 0 + 0 = 0

• 0 + 1 = 1

• 1 + 0 = 1

• 1 + 1 = 10

4-bit Addition

• 4 + 4 = 8

• 4 + 8 = C

• 8 + 7 = F

• F + E = 1D “carry”

Number Conversions