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Department of Computer and Information Science, School of Science, IUPUI

Department of Computer and Information Science, School of Science, IUPUI. CSCI 230. Information Representation: Negative Integer Representation . Dale Roberts, Lecturer IUPUI droberts@cs.iupui.edu. Negative Numbers in Binary.

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Department of Computer and Information Science, School of Science, IUPUI

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  1. Department of Computer and Information Science,School of Science, IUPUI CSCI 230 Information Representation: Negative Integer Representation Dale Roberts, Lecturer IUPUI droberts@cs.iupui.edu

  2. Negative Numbers in Binary • Four different representation schemes are used for negative numbers • Signed Magnitude • Left most bit (LMB) is the sign bit : • 0  positive (+) • 1  negative (-) • Remaining bits hold absolute magnitude Example: 210  0000 0010b -210 1000 0010b Q: 0000 0000 = ? 1000 0000 = ? Try, 1000 0100b = -410

  3. 1’s Complement • One’s Complement • Left most bit is the sign bit : • 0  positive (+) • 1  negative (-) • The magnitude is Complemented Example: 210 0 000 0010b -210  1 111 1101b Exercise: try - 410using 1’s Complement Q: 0000 0000 = ? 1111 1111 = ? Solution: 410 = 0 0000100b -410 = 1 1111011b

  4. 2’s Complement • 2’s Complement • Sign bit same as above • Magnitude is Complemented first and a “1” is added to the Complemented digits • Example: • 210 0 000 0010b • 1’s Complement  1 1111101b • +1 • -210 1 111 1110b • Exercise: try -710using 2’s Complement • 710 • 1’s Complement  • +1 • -710  0000 0111b 11111000b • 1111 1001b

  5. 2’s Complement 710 = 0000 0111b 310 = 0000 0011b 1’s complement 1111 1100b 2’s complement 1111 1101b -310 7+(-3)  0000 0111 + 1111 1101 • Example: 7+(-3) [hint]: A – B = A + (~B) +1 1 1111 111 carry • ignore 1 0000 0100  0000 0100 410

  6. Three Representation of Signed Integer

  7. Negative Numbers in Binary (cont.) • Excess Representation • For a given fixed number of bits the range is remapped such that roughly half the numbers are negative and half are positive. Example: (as left) Excess – 8 notation for 4 bit numbers • Binary value = 8 + excess-8 value • MSB can be used as a sign bit, but • If MSB =1, positive number • If MSB =0, negative number • Excess Representation is also called bias

  8. Fundamental Data Types • With vs. without using sign bit • For a 16 bit binary pattern:

  9. Fundamental Data Types • Four Data Typesin C(assume 2’s complement, byte machine) • Note: 27 = 128, 215 =32768, 215 = 2147483648 • Complex and double complex are not available

  10. Acknowledgements • These slides where originally prepared by Dr. Jeffrey Huang, updated by Dale Roberts.

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