Partial preview of the text
Download Fundamentals of computer application and more Study notes Computer Fundamentals in PDF only on Docsity!
History anal Rvotution of Computing System is take the otal nnmber M0 Ty thin number: va) For example, ‘The righunost digit represents the yale OF ‘rhe nest ait tothe Lol represents the vate oF 8! ‘Phe tettmost digit represents the vate oF 87 OND: ‘To find the decimal equivalent oF the oetal muumber, You multiply eaely ditt by We corresponding power of 8 ane then sum apy the results! Ges eas sor Grsraee Ad 102 = 280, Mo is equivalent to the deel omputing ayatenns, particularly tn the (a). So, the vetal number nal number 240: etal numbers were commonly used fn early ¢ addresses and ditt, representation of memory Hexadecimal Number System yer system (base=10), each digit can take on one oF sixteen In the hexadecimal numb possible: values: 0-9 and A-B, That isatter 0-9, 10 is represented ax Ay TL aw W.A2ane, 13 as D, [4 as B, 15 as F The value ofa hexndecinnal mumber is determined by the position of its digits relative (0 the hexadecimal point: For example, let's take the hexadecimal number TART, tn this numbers ‘The rightmost diz! The next digit to the lel it represents the value of 16"). ft represents the value of 16! (16). The next digit represents the value of 16° (256). The leftmost digit represents the value of 16’ (4096). To find the decimal equivalent of the hexadecimal number, its corresponding power ‘of 16 and then sunt Up the results: (5 16") +G* 16) + (10* 16) (16) = 15+ 48+ 2560 + 4096 = S719. JASE is equivalent to the decimal nuniber 5719. din computer science and digital elect data, and colors. ‘They are preferred of conversion to and from you multiply euch digit by So, the hexadecimal number’ ‘Hexadecimal numbers are commonly use’ particularly for representing memory addresses, over binary and ‘octal numbers for their compactness and ease binary representation. ALONIeS, ee History and Evolution of Computing System Examples Example 1: Conyert 13 to Binary Divide 13 by 2: Quotient =6, Remainder = 1 Divide 6 by 2: Quotient = 3, Remainder = 0 Divide 3 by 2: Quotient = 1, Remainder = | Divide I by 2: Quotient =0, Remainder= 1 v Reading the remainders from bottom to top, we get 1101. “ Thus, the binary representation of 13 is 1101. Example 2: Convert 29 to Binary Divide 29 by 2: Quotient = 14, Remainder=1 Divide 14 by 2: Quotient = 7, Remainder =0 Divide 7 by 2: Quotient =3, Remainder = Divide 3 by 2: Quotient = 1, Remainder = Divide 1 by 2: Quotient = 0, Remainder = 1 Reading the remainders from bottom to top, we get 11101. Thus, the binary representation of 29 is 1 1101. Example 3: Convert 50 to Binary Divide 50 by 2: Quotient = 25, Remainder = 0 Divide 25 by 2: Quotient= 12, Remainder = 1 Divide 12 by 2: Quotient = 6, Remainder = 0 Divide 6 by 2: Quotient = 3, Remainder = 0 Divide 3 by 2: Quotient = I, Remainder = 1 Divide 1 by 2: Quotient = 0, Remainder = 1 Reading the remainders from bottom to top, we get 110010. Thus, the binary representation of 50 is 110010. Example 4: Convert 13.625 to Binary 1. Convert the integer part (13): 
