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ECE 291

ECE 291. Lecture 2: Number Systems & x86 Instructions Constantine D. Polychronopoulos Professor, ECE Office: 463 CSRL. Spring 2000. Number Systems - Review ECE 290!!. Decimal numbers (or base 10 system) - Notation: 0,1,…9: Example: 378 = 3 * 10 2 + 7 * 10 1 + 8 * 10 0

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ECE 291

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  1. ECE 291 Lecture 2: Number Systems & x86 Instructions Constantine D. Polychronopoulos Professor, ECE Office: 463 CSRL Spring 2000 ECE 291 -- Spring 2000

  2. Number Systems - Review ECE 290!! • Decimal numbers (or base 10 system) - Notation: 0,1,…9: • Example: 378 = 3 * 102 + 7 * 101 + 8 * 100 • Binary numbers (or base 2 system) - Notation: 0 and 1: • Example: (001101)2 = 1 * 23 + 1 * 22 + 0 * 21 + 1 * 20 = 8+4+1=(13)10 • Hexadecimal numbers (or base 16 system) - Notation: 0..9,A,B,C,D,E,F: • Example: 52A4F = 5*164 + 2*163 + 10*162 + 4*161 + 15*160 • Many other representations • BCD (Binary Coded Decimal): decimal numbers represented in binary notation with each decimal digit represented by its 4-bit binary encoding: • Example: 728 in BCD is 0111 0010 1000 ECE 291 -- Spring 2000

  3. Base Conversion • Always easy to convert from any base b to decimal: just compute the sum of products - result is in decimal. • Converting from decimal to base b: Successive division or (remainder) decimal with the largest power of b - successive quotients form base b representation. • Example: Convert 77 to binary representation. • Divide 77 by 64 (26) - Q = 1 R=13 • Divide 13 by 8 (23) - Q = 1 R=5 • Divide 5 by 4 (22) - Q = 1 R=1 • Divide 1 by 1 (20) - Q = 1 R=0 --- DONE • Result: 77 = 1 0 0 1 1 0 1 • Put 1’s where Q=1 and 0’s in the remaining positions ECE 291 -- Spring 2000

  4. Converting Fractional Part • 1- Multiply fraction with base • 2- Save integer digit (if any) • 3- Repeat until remainder=0 or accuracy is obtained • 4- The successive digits form the converted fractional representation • Example: Converting .173 to octal representation • .173 X 8 = 1.384 Save 1 • .384 X 8 = 3.072 Save 3 • .072 X 8 = 0.576 Save 0 • .173 in base 10 = .130… octal ECE 291 -- Spring 2000

  5. Radix-1 & Radix Complement Representation • One’s complement representation: • Subtract n-bit binary representation from n-bit all 1’s (radix-1) • Two’s complement representation: • As in One’s complement + add 1 to the result (radix) • One of the problem with (radix-1) complement representation is inability to uniquely represent zero. • Two’s complement gives you the inverted (negated) number: if you add a number and its (radix) complement discarding any overflow, the result is ZERO! ECE 291 -- Spring 2000

  6. Signed & Unsigned Representations • First bit in binary rep. is sign bit: • s=0: positive (+) • s=1: negative (-) • Two quick schemes to represent a negative number N (any of them will work): • Invert all bits then add 1 (2’s complement) • Scan N from right to left: copy 0’s, copy first 1, invert the rest • Sign-extending a number: copy sign bit into extra leftmost positions ECE 291 -- Spring 2000

  7. Memory Objects & Data Types • Data Types • Numbers • bit (eg: 1) • nibble = 4 bits • DB:byte = octet = 8 bits • DW:Word = 2 bytes = 16 bits (80x86 terminology) • DD:DoubleWord = 4 bytes = 32 bits (80x86 terminology) • Intel uses little endian format (i.e., LSB at lower address) • Signed Integers (2's complement) ECE 291 -- Spring 2000

  8. Memory Objects (Cont.) • Text • Letters and characters (7-bit ASCII standard) • 'A'=65=0x41 • Extended ASCII (8-bit) allows for extra 128 graphics/symbols) • Collection of characters = Strings • Collection of Strings = Documents • Programs • Commands (MOV, JMP, AND, OR, NOT) • Collections of commands = procedures/functions/subroutines • Collection of subroutines = programs ECE 291 -- Spring 2000

  9. Memory Objects (Cont.) • Floating point numbers (covered later) • Images (GIF, TIF, JPG, BMP) • Video (MPEG, QuickTime, AVI) • Audio (voice, music) ECE 291 -- Spring 2000

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