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Computer SCIENCE

Data Representation and Machine Concepts. Computer SCIENCE. Section 1.6. Instructor: Lin Chen. Sept 2013. 1 Data Storage. 1.6 Storing Integers. Two’s Complement Excess Notation.

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Computer SCIENCE

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  1. Data Representation and Machine Concepts Computer SCIENCE Section 1.6 Instructor: Lin Chen Sept 2013

  2. 1 Data Storage 1.6 Storing Integers Two’s Complement Excess Notation http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-01-unified-engineering-i-ii-iii-iv-fall-2005-spring-2006/comps-programming/number_systems.pdf Pearson Custom: Computer Science, Data Representation and Machine Concepts

  3. 1.6 Storing Integers Two’s Complement Use a fixed number of bits to represent each of the values in the system First bit is used to represent the sign, 1 represents negative number, 0 represent nonnegative number A negative number is represented by inverting the bits of its corresponding positive number in each place, then add 1 to the inverted number Suppose to use 4 bits to represent the number 01112 = 7 10 10002 +1 10012 = -7 10

  4. 1.6 Storing Integers Two’s Complement Write the two’s complement notation for -6, -3, -1.

  5. 1.6 Storing Integers Two’s Complement Four Bits

  6. 1.6 Storing Integers Two’s Complement Addition 7 – 2 = 7 + (-2) = ? 0111 1110 + 10101

  7. 1.6 Storing Integers Two’s Complement Addition 7 – 2 = 7 + (-2) = ? 0111 1110 + 10101 Use four bits 01012 = 510

  8. 1.6 Storing Integers Two’s Complement Use two’s complement notation to calculate: 7 – 5 = ? -3 – 4 = ? 6 – 4 = ? -2 – 5 = ?

  9. 1.6 Storing Integers Two’s Complement What is the range of numbers that can be represented using the 2’s complement? Answer: 2N-1 – 1 to -2N-1 N is the number of bits Three bits: 3 to -4 Four bits: 7 to -8 Eight bits: ?

  10. 1.6 Storing Integers Two’s Complement List all the number with the two’s complement notation using 3 bits Express 16 - -16 with the two’s complement notation using 8 bits

  11. 1.6 Storing Integers Two’s Complement Overflow Calculate 5 + 4 with two’s complement notation using 4 bits

  12. 1.6 Storing Integers Excess Notation Steps: Add the excess value 2N-1 to the number, where N is the number of bits used Convert the resulting number into binary format Suppose use 4 bits 2 0010 + 8 = -6 24-1

  13. 1.6 Storing Integers Two’s Complement Write -8 to 7 with excess notation with 4 bits Write -4 to 3 with excess notation with 3 bits

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