Hexadecimal Arithmetic PDF

Summary

These lecture notes cover hexadecimal arithmetic, including addition, subtraction, multiplication, and division. Examples and tables are included. The notes are suited for undergraduate-level computer science or mathematics courses.

Full Transcript

Hexadecimal arithmetic Lecturer: Jay A. Abaleta Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = Hexadeci 13, E = 14, F = 15. Also called b...

Hexadecimal arithmetic Lecturer: Jay A. Abaleta Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = Hexadeci 13, E = 14, F = 15. Also called base 16 number system. mal Each position in a hexadecimal number Number represents a 0 power of the base (16). Example − 160 System Last position in a hexadecimal number represents an x power of the base (16). Example − 16x where x represents the last position - 1. The Hexadecimal Addition table The Hexadecimal Addition 6+3 = 9 10+11 = 21 21/16 =Q-1 R-5 1+4+1 = 6 The Hexadecimal Subtraction The subtraction of hexadecimal numbers follow the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. The Hexadecimal Subtraction The Hexadecimal Multiplication The multiplication process of Hexadecimal numbers are same as other number systems. You can verify your result by using this. The points you should keep in mind while multiplying hexadecimal numbers: If the sum exceeds 15 ( 0,1,2,3,4,5,6,7,8,9, A,B,C,D,E,F) you need to evaluate the equivalent hexadecimal value. Divide the number by 16 and find its equivalent hexadecimal value. Quotient is going to be carry while remainder taken as sum The Hexadecimal Multiplication Hexadecimal Multiplicatio n A*5 10*5=50 50/16 Q3, R2, S2 A*7 10*7 =70 70/16 = Q4, R6, S9 13(D)*5=65 65/16 = Q4, R1, S1 13(D)*7 = 91 91/16 = Q5, R=11(B),S- 15(F) The Hexadecimal Division To solve division examples you must know how to perform multiplication on octal numbers. Example: Decimal - 11(B)*3 = 33 33/16 = Q2,R1= S21 11(B)*6 = 66 66/16 = Q4,R2, S42

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