Applied physics iii lecture2 number_systemsii
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Transcript of Applied physics iii lecture2 number_systemsii
Applied physics III
Number systems: Arithmetic Operations
by Benson Mbuya1
Review of basic concepts of arithmetic
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Addition and subtraction of binary numbers
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Add the binary numbers 01010 and 10111
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Subtract 111 from 10001
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Hexadecimal Addition & Subtraction• Hexadecimal Addition
—Carry generated• Hexadecimal Subtraction
—Borrow weight 16
Hexadecimal AdditionCarry 1
2AC6 6+5=11d Bh + 92B5 C+B=23d 17h
BD7B A+2+1=13d Dh2+9=11d Bh
Hexadecimal SubtractionBorrow 111
92B5 21-6=15d Fh - 2AC6 26-C=14d Eh
67EF 17-A=7d 7h8-2=6d 6h
Octal Addition & Subtraction• Octal Addition
—Carry generated• Octal Subtraction
—Borrow weight 8
Octal AdditionCarry 1
7602 2+1=3d 3O + 5771 0+7=7d
7O 15573 6+7=13d 15O
1+7+5=13d 15O
Octal SubtractionBorrow 11
7602 2-1=1d 1O - 5771 8-7=1d 1O
1611 13-7=6d 6O6-5=1d 1O
Addition and subtraction of hexadecimal numbers
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Representing negative numbers in a computer
• By convention the leftmost bit (or most significant bit) is considered the sign bit.
• A value of 0 in the sign bit indicates a positive number,
• whereas a 1 indicates a negative number.
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examples
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ONE’S COMPLEMENT
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2’s Complement
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references• Chapter 30, Teach yourself electronics, 3rd ed,
Stan Gibilisco.• Chapter 4, digital electronics demystified, Myke
Predko.• Chapter 18, Schaums outline: basic mathematics
with applications to science and technology, Kruglak, Moore.
• http://www.electronics.dit.ie/staff/tscarff/number_systems/number_systems.html
• http://active.tutsplus.com/tutorials/coding-concepts/number-systems-an-introduction-to-binary-hexadecimal-and-more/
• http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary
• http://active.tutsplus.com/tutorials/coding-concepts/number-systems-an-introduction-to-binary-hexadecimal-and-more/
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