9. Appendix B X

# 9. Appendix B X - Digital Design Digital By Frank Vahid...

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Digital Design Digital Design By Frank Vahid By Frank Vahid     Pima Community College George Haines, Instructor Wednesday 10/20/10 Appendix B Number Representation

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Appendix B Appendix B Additional Topics in Binary Number Systems Additional Topics in Binary Number Systems B.1 Introduction B.2 Real Number Representation EXAMPLE B.1 Converting real numbers from decimal to  binary with the subtraction method Converting real decimal fractions to binary by the dividing  by 2 method B.3 Fixed Point Arithmetic B.4 Floating Point Representation The IEEE 754-1985 Standard EXAMPLE B.2 Converting decimal real numbers to floating  point
B.1 Introduction We have covered how to convert a decimal integer to a binary through the subtraction method and the divide-by-two method . However, numbers we use in digital systems may not always be represented as whole numbers. In this Appendix, we will discuss how real numbers, whole and fractions , are represented in binary, and discuss methods that modern digital systems use to work real numbers.

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fappB_0 fappB_01 fappB_01 B.2 Real Number Representation The dot in the middle of the digits is the decimal point. The decimal point separates the fractional component of the number from the whole part. The weights of each digit to the left of the decimal point (the whole part) are in increasing powers of 10, the weights of each digit to the right of the decimal point (the fractional part) are weighted in negative powers of 10.
fappB_02 We can represent real numbers in binary in a similar manner. Instead of a decimal point, real numbers feature a binary point . Digits to the left of the binary point are weighted with positive powers of 2. The digits to the right of the binary point are weighted in negative powers of 2. E.g. the binary number 10.1101 = 1*2

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## 9. Appendix B X - Digital Design Digital By Frank Vahid...

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