Computer Architecture & Organization Lecture 1 PDF

Computer Architecture Duhok Polytechnic University & Organization Duhok Technical Institute Dept. of Information Technology First Stage Lecturer ~ Walat Ali Ahmed...

Computer Architecture Duhok Polytechnic University & Organization Duhok Technical Institute Dept. of Information Technology First Stage Lecturer ~ Walat Ali Ahmed LEC.1 NUMBER SYSTEMS AND CODES Computer Architecture & Organization  In computer engineering, computer architecture is a set of rules and methods that describe the functionality, organization and implementation of computer systems. Number systems  The decimal system has ten digits (0 to 9) inclusive with the base of (10). A decimal number such as (384.85)₁₀ can be expressed in the following form.  (384.85)₁₀ =3x10²+8x10¹+4x10 ⁰+ 8x10⁻¹ +5x10⁻²  While the binary number system has a base of 2 and only two digits (0, 1) 27 26 25 24 23 22 21 20 12810 6410 3210 1610 810 410 210 110 Dec. No 0 010 1 110 1 0 210 1 1 310 1 0 0 410 1 0 1 510 1 1 0 610 1 1 1 710 1 0 0 0 810 1 0 0 1 910 1 0 1 0 1010 1 0 1 1 1110 1 1 0 0 1210 1 1 0 1 1310 1 1 1 0 1410 1 1 1 1 1510 1 0 0 0 0 1610 1 0 0 0 1 17  Try writing the binary numbers from (100102 to 10000002)  The word bit is a contraction of the words binary digit. The binary number (100102) is a 5- bit binary number, the first place on the right is called the least significant bit (LSB) and the left-most place is called the most significant bit (MSB) as shown below.  Using eight bits we can count in binary to ( 111111112 or 25510 ) or using three bits we can count in binary to (1112 or 710), including 0002 we have eight different combinations.  Convert (101.11)2 to decimal number.  (N)= 1 x 2² + 0 x 2¹ + 1 x 2⁰ + 1 x2 ⁻¹+ 1 x 2 ⁻²  = 4.0 + 0.0 + 1.0 + 0.5 + 0. 25 = (5.75)₁₀  The other number systems of some importance are the Octal or the base 8 system and has 8 digits from ( 0 to 7 ) inclusive as in figure (1.1) , a typical Octal number is (26.2)₈ and its decimal value is given by.  (26.2)₈ = 2x8 ¹+ 6x8⁰ +2x8 ⁻¹ = 16.0 + 6.0 + 0.25 = (22.25)₁₀ Octal Binary (0) ₈ 000 (1)₈ 001 (2)₈ 010 (3)₈ 011 (4)₈ 100 (5)₈ 101 (6)₈ 110 (7)₈ 111 Figure (1-1) Octal / Binary conversion table  Hexadecimal system  there are 16 digits (0,1,2,3,4,5,6,7,8,9,A,B.C.D.E.F) , and the base of 16.  Figure (1.2) Hexadecimal / Binary / Decimal / Octal conversion table  A typical hexadecimal number (B3.C) ₁₆has a decimal value which is given by: (B3.C) ₁₆ = B x 16 ¹ + 3 x 16 ⁰ + C x 16 ⁻¹ = 11 x 16 + 3 x 1 + 12 x (1/16) = 176 + 3 + 12 x (0.0625) = 176 + 3 + 0.75 = (179.75)₁₀