Ch 2. Instructions: Language of the Computer -(5)

2. Binary Number Basic

Unsigned Binary Integers

• Range: 0 to +2^n - 1
• Using 32 bits
  • 0 to +4,294,967,295
• Ex)
  • 0000 0000 0000 0000 0000 0000 0000 1011
    = 0 + ••• + 1×2^3 + 0×2^2 + 1×2^1 + 1×2^0
    = 0 + ••• + 8 + 0 + 2 + 1 = 11

Negative Number Representations

Sign Magnitude	One’s Complement	Two’s Complement
000 = +0	000 = +0	000 = +0
001 = +1	001 = +1	001 = +1
010 = +2	010 = +2	010 = +2
011 = +3	011 = +3	011 = +3
100 = -0	100 = -3	100 = -4
101 = -1	101 = -2	101 = -3
110 = -1	110 = -1	110 = -2
111 = -2	111 = -0	111 = -1

• Two’s Complement
  • 0을 나타내는 숫자가 하나
  • 더 많은 숫자를 표현
  • ease of operations
• Exercise
  • -11: 0 000 1011
  • signed magnitude
    • 1 000 1011
  • one’s complement
    • 1 111 0100
  • two’s complement
    • 1 111 0101

2s-Complement Signed Integers

• Range: -2^n-1 to +2^n-1 - 1
• Using 32 bits
  • -2,147,483,648 to +2,147,483,647
• Ex)
  • 1111 1111 1111 1111 1111 1111 1111 1100
    = -1×2^31 + 1×2^30 + ••• + 1×2^2 + 0×2^1 + 0×2^0 = -2,147,483,648 + 2,147,483,644 = -4

Signed Negation

• Complement and add 1
• Ex) Negate +2
  • +2 = 0000 0000 ••• 0010
  • -2 = 1111 1111 ••• 1101 + 1 = 1111 1111 ••• 1110