CSCI 235 — Sections 2.1 to 2.3

CMU 15-215 Video to view

• Bits, Bytes, and Integers 1
• Bits, Bytes, and Integers 2

Numbers

• Bases of Java literals
  • decimal 235
  • octal 0235710
  • hexadecimal 0x235eA
  • binary 0b0110001010111 — not in C (but in GCC)
  • Examples
    • decimal ↔ binary and hexadecimal
      • 235
      • 2018
    • binary ↔ octal ↔ hexadecimal
      • 0b1101001101
      • 0666
      • 0xE1E10
• Integer types of Java — C also has unsigned types
  • byte, 8 bits — in C99, int8_t
  • short, 16 bits — in C99, int16_t
  • int, 32 bits — in C99, int32_t
  • long, 64 bits — in C99, int64_t
  • char, 16 bits — in C99, uint16_t
• Bitwise operators of Java   ~, &, |, and ^
  • ~235
  • 235 & 100
  • 235 | 100
  • 235 ^ 100
• Representation of negative numbers — two’s complement only
  • Negative weight to the most significant bit
  • You must know the number of bits
  • Examples in 10-bit two’s complement
    • 235
    • -235
    • -100
    • -1
• Shift operators of Java — <<, >>, >>> (not in C)
  • Arithmetic vs logical right shift
  • You must know the number of bits
  • Examples in 12-bit. Assume are all signed.
    • 235 >> 2
    • -235 >> 2
    • 235 << 2
• Widening and narrowing casts
  • Java defines widening and narrowing casts
  • In C, unsigned makes this difficult; however, narrowing is fine, if input within the output range
  • References for C
    • CERT recommendations for secure coding
    • C in a Nutshell explanation of the rules
• Overflow — signed and unsigned arithmetic
  • If it makes no sense to the 5th grader, it is wrong!
  • Examples in 10-bit signed
    • 235 + 888
    • 235 + 400
    • -235 + -100
  • Examples in 10-bit unsigned
    • 235 + 888
    • 235 + 400
• Optimizing multiplication and division by constants
  • X<<n multiplies by 2ⁿ — if result in range
  • X>>n divides by 2ⁿ — if result in range, but rounding is downward not toward zero
  • Z = X*1000 ; is probably slower than T = X<<3 ; Z = X<<10 - T - T - T ;
  • Practice Problem 2.40 (p. 40)