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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