This follows from the fact that twos complement

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Unformatted text preview: ion as a function 42 Quantity CHAPTER 2. REPRESENTING AND MANIPULATING INFORMATION Word Size Û 32 64 0xFFFFFFFF 0xFFFFFFFFFFFFFFFF 4,294,967,295 18,446,744,073,709,551,615 0x7FFFFFFF 0x7FFFFFFFFFFFFFFF 2,147,483,647 9,223,372,036,854,775,807 0x80000000 0x8000000000000000 2,147,483,648 9,223,372,036,854,775,808 0xFFFFFFFF 0xFFFFFFFFFFFFFFFF 0x00000000 0x0000000000000000 ÍÅ Ü Û ÌÅ Ü Û ÌÅ Ò Û 1 ¼ 8 0xFF 255 0x7F 127 0x80 128 0xFF 0x00 16 0xFFFF 65,535 0x7FFF 32,767 0x8000 32,768 0xFFFF 0x0000 Figure 2.9: “Interesting” Numbers. Both numeric values and hexadecimal representations are shown. ¾Í Û (for “binary to unsigned,” length Û): ¾Í Û ´Üµ Û ½ ¼ ܾ (2.1) (In this equation, the notation “ ” means that the left hand side is defined to equal to the right hand side). That is, function ¾Í Û maps length Û strings of 0s and 1s to nonnegative integers. The least value is given by bit vector ¼¼ ¡ ¡ ¡ ¼ having integer value ¼, and the greatest value is...
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This note was uploaded on 09/02/2010 for the course ELECTRICAL 360 taught by Professor Schultz during the Spring '10 term at BYU.

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