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Chapter 5 NUMBER REPRESENTATION AND ARITHMETIC CIRCUITS

Chapter 5 NUMBER REPRESENTATION AND ARITHMETIC CIRCUITS. 5.1 Number representation and arithmetic circuits. Octal and hexadecimal representations The positional number representation can be used for any radix. If the radix is r, the number has the value V(K) =

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Chapter 5 NUMBER REPRESENTATION AND ARITHMETIC CIRCUITS

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  1. Chapter 5NUMBER REPRESENTATION AND ARITHMETIC CIRCUITS

  2. 5.1 Number representation and arithmetic circuits • Octal and hexadecimal representations • The positional number representation can be used for any radix. • If the radix is r, the number has the value V(K) = • Besides decimal (r=10) and binary(r=2) numbers, two other radices are useful – 8 and 16. • Numbers with radix 8 are Octal numbers(0-7). • Numbers with radix 16 are Hexadecimal numbers(0-15).

  3. Figure 5.1. Numbers in different systems.

  4. Octal Conversions • Binary to octal • Group binary positions in groups of three • Write the octal equivalent • Octal to binary • Reverse the process • Octal to decimal • Multiply by weighting factors • Decimal to octal • Successive division 14

  5. Hexadecimal Conversions • Binary-to-hexadecimal conversion • Group the binary in groups of four • Write the equivalent hex digit • Hexadecimal-to-binary conversion • Reverse the process 16

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