Binary Number System

Introduction

• Computers operate on binary logic (not decimal)
• Study of binary number system is essential

Basics of Binary Number System

• Base (radix) = 2
• Digits available: 0, 1 (bits)

Example of a Binary Number

• Binary number: 10101
• Weight of positions:
  • 2^0
  • 2^1
  • 2^2
  • 2^3
  • 2^4
• Representation:
  • 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0
  • Calculation: 16 + 0 + 4 + 0 + 1 = 21 (decimal equivalent)

Binary Point

• Binary number example: 10101.11
• Weights for binary point:
  • 2^0, 2^1, 2^2, 2^3, 2^4
  • 2^-1, 2^-2
• Representation:
  • 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 + 1 * 2^-1 + 1 * 2^-2

MSB and LSB

• MSB: Most Significant Bit (leftmost)
• LSB: Least Significant Bit (rightmost)
• Example with binary number 10101 (decimal 21)
  • Changing LSB (1 to 0): 10100 (decimal 20)
  • Changing MSB (1 to 0): 00101 (decimal 5)
  • Greater difference when MSB is changed
• Significance:
  • B0 (rightmost) least significant
  • B4 (leftmost) most significant

Units of Data

• Bit: smallest unit of data
• Nibble: 4 bits
  • Represents binary coded decimal (BCD) and hexadecimal numbers
• Byte: 8 bits
• Word: 16 bits
• Double Word: 32 bits
  • 1 word = 2 bytes
  • 1 double word = 4 bytes

Conclusion

• End of presentation
• See you in the next one