1 / 8

Lecture 2: Number Systems

Lecture 2: Number Systems. Supplementary Notes Complements Floating-point Numbers. Complements. “Find the complement of a number” is the short way of saying “find the negated value in the complement system”. For example, the two questions below are equivalent.

paniz
Download Presentation

Lecture 2: Number Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 2: Number Systems Supplementary Notes • Complements • Floating-point Numbers Number Systems Supplementary Notes

  2. Complements • “Find the complement of a number” is the short way of saying “find the negated value in the complement system”. • For example, the two questions below are equivalent. • [4-bit base-2] Find the 1’s complement of 0110. Answer: 1001. • [4-bit base-2] If x is (0110)1s, what is -x in 1’s complement form? Answer: (1001)1s • So, “find the 1’s complement of 0110” is not asking for “how is 0110 represented in 1’s complement”. Complements

  3. Complements • More examples: • [8-bit base-2] Find the 1’s complement of 101. Answer: 11111010. • [8-bit base-2] Find the 1’s complement of 11001000. Answer: 00110111. • [8-bit base-2] How is (101)2 represented in 1’s complement? Answer: 00000101. • [8-bit base-2] How is -(101)2 represented in 1’s complement? Answer: 11111010. • [8-bit base-2] Find the 2’s complement of 111000. Answer: 11001000. Complements

  4. Complements • More examples: • [8-bit base-2] What is (111)2 in 2’s complement form? Answer: 00000111. • [8-bit base-2] What is -(111)2 in 2’s complement form? Answer: 11111001 • [6-bit base-2] What is (14)10 in 1’s complement form? Answer: (001110)1s. • [6-bit base-2] What is (-14)10 in 2’s complement form? Answer: (110010)2s. Complements

  5. Complements • More examples: • [3-digit base-10] Find the 9’s complement of 25. Answer: 974. • [3-digit base-10] Find the 10’s complement of 123. Answer: 877. • [3-digit base-8] Find the 7’s complement of 712. Answer: 065. • [3-digit base-8] Find the 8’s complement of 123. Answer: 655. • [2-digit base-7] What is the radix complement of 15? Answer: 52. • [3-digit base-9] What is the diminished radix complement of 814? Answer: 074. Complements

  6. Floating-point Numbers • Assume a 10-bit floating-point scheme with: 1-bit sign, 5-bit normalised mantissa, and 4-bit exponent. • What is this value: 1 11000 1001 ? • Sign bit is 1, so value is negative. • Mantissa is (0.11000)2, or (0.75)10 • What about exponent? • If exponent is unsigned, then exponent = 9. • If exponent is signed, and sign-and-magnitude is used, then exponent = -1. • If exponent is signed, and 1’s complement is used, then exponent = -6. • If exponent is signed, and 2’s complement is used, then exponent = -7. Floating-point Numbers

  7. Floating-point Numbers • Therefore, • If exponent is unsigned, then value is -(0.11)2 x 29, or -(110000000)2, or -(384)10. • If exponent is in sign-and-magnitude, then value is -(0.11)2 x 2-1, or -(0.011)2, or (0.375)10. • If exponent is in 1’s complement form, then value is -(0.11)2 x 2-6, or -(0.00000011)2. • If exponent is in 2’s complement form, then value is -(0.11)2 x 2-7, or -(0.000000011)2. Floating-point Numbers

  8. End of file

More Related