CSCI 235 — Gonig binary

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

The bases of integer literals

• Bases of Java literals
  • decimal 2018
  • octal 0235710
  • hexadecimal 0x235eA
  • binary 0b0110001010111 — accepted in C++11, C#, Python and supported in gcc extensions for C
• 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 ^
  • Examples to do
    • ~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 to do in 10-bit two’s complement
    • 235
    • -235
    • -100
    • -1
  • C99 requires the use of two’s complement. Older versions of C did not.
• Shift operators of Java — <<, >>, >>> (not in C)
  • Arithmetic vs logical right shift
  • You must know the number of bits
  • Examples to do 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
• Overflow — signed and unsigned arithmetic
  • If the result is out-of-range, overflow will happen
• 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 ;