4.2 Numbers and Bits

4.2 Numbers and Bits

4.2.1 Reading and Web Sites

1. Data Types. Read IA-32 Volume 1 [3] Pages 4-1 through 4-10 Sections 4.1 -- 4.5
2. Flags. Read IA-32 Volume 1 [3] Pages 3-21 -- 3-22. Section 3.4.3.1 about bits CF, ZF, SF, and OF.
3. Binary Arithmetic Instructions. Read IA-32 Volume 1 [3] Pages 7-12 -- 7-13. Sections 7.3.2 -- 7.3.3
4. Logical Instructions. Read IA-32 Volume 1 [3] Pages 7-15. Sections 7.3.5
5. Floating-point. Read IA-32 Volume 1 [3] Pages 4-15 through 4-21 Sections 4.8 -- 4.8.3.2
6. Browse at IA-32 Volume 1 [3] After page 5-4.
   • Section 5.1.2 Binary Arithmetic Instructions
   • Section 5.1.4 Logical Instructions
   • Section 5.1.5 Shift and Rotate Instructions
   • Section 5.1.6 Bit and Byte Instructions
   • Section 5.1.7 Control Transfer Instructions
   • Section 5.2.2 x87 FPU Basic Arithmetic Instructions

4.2.2 Notes

• Unsigned (positive) numbers
  • Numbers, decimal, binary, and hexadecimal

     

     

    Conversion table for small numbers

    Binary	Octal	Decimal	Hexadecimal
    0000	0	0	0
    0001	1	1	1
    0010	2	2	2
    0011	3	3	3
    0100	4	4	4
    0101	5	5	5
    0110	6	6	6
    0111	7	7	7
    1000	10	8	8
    1001	11	9	9
    1010	12	10	A
    1011	13	11	B
    1100	14	12	C
    1101	15	13	D
    1110	16	14	E
    1111	17	15	F

  • Math, add and subtract
  • Math, multiply and divide by 2 (Popsicle toes [2])
  • Fixed word lengths 8, 16, 32, 64, and 128 bits.
    Possible values. 2ⁿ
    Range. 2ⁿ-1
  • 2¹⁰, 1024 is about equal to 1000
  • 2²⁰, 1048576 is about equal to 1,000,000
  • overflow, carry bit, zero bit

   

  Unsigned number range

  Bits	Minimum	Maximum
  n	0	2n-1
  4	0	7
  8	0	255
  16	0	65535
  32	0	4294967295
  64	0	18446744073709551615
  128	0	340282366920938463463374607431768211455

• Signed, ones complement, and twos complement numbers
• Twos complement numbers
  • Range
    • Possible values: 2ⁿ
    • Possible positive values: 1 <==> 2^n-1-1
    • Zero.
    • Possible negative values: -2^n-1 <==> -1
    • Range: -2ⁿ-1 <==> 2^n-1-1

     

    Twos complement range

    Bits	Minimum	Maximum
    n	-2n-1	2n-1-1
    4	-8	7
    8	-128	127
    16	-32768	32767
    32	-2147483648	2147483647
    64	-9223372036854775808	9223372036854775807

  • Twos complement operation
  • Addition
  • Subtraction
  • Multiplication by 2
  • Division by 2
  • overflow, carry bit, zero bit, & sign bit
• Extended precision arithmetic.
  • Base 256
  • Base 65536
  • Base 4294967296
  • Base 18446744073709551616
• Logical operations
  • AND, OR, XOR, and NOT

     

    Logical Functions

    a	b	a AND b	a OR b	a XOR b	NOT a
    0	0	0	0	0	1
    0	1	0	1	1	1
    1	0	0	1	1	0
    1	1	1	1	0	0

  • shifting, bit packing
  • bit banging instructions
  • I/O control registers

4.2.3 Lab Assignment

4.2 Numbers and Bits