SLIDE 1
Arithmetic on N
Addition is space-efficient.
- eg. Base 10 coding of N. ’carry propagation’ procedure for +.
Coding addition Sasha Rubin Cornell REU 2009 Arithmetic on N - - PowerPoint PPT Presentation
Coding addition Sasha Rubin Cornell REU 2009 Arithmetic on N - - PowerPoint PPT Presentation
Coding addition Sasha Rubin Cornell REU 2009 Arithmetic on N Addition is space-efficient. eg. Base 10 coding of N . carry propagation procedure for +. Arithmetic on N Addition is space-efficient. eg. Base 10 coding of N . carry
SLIDE 2
SLIDE 3
Arithmetic on N
Addition is space-efficient.
- eg. Base 10 coding of N. ’carry propagation’ procedure for +.
But the usual multiplication procedure is not space-efficient. More is true. There is no space-efficient coding of (N, ×).
SLIDE 4
Space-efficient presentations of +
Basic systems: base 10, base 2, . . .
SLIDE 5
Space-efficient presentations of +
Basic systems: base 10, base 2, . . . Non-standard systems: Fibonacci, −2, . . .
SLIDE 6
Space-efficient presentations of +
Basic systems: base 10, base 2, . . . Non-standard systems: Fibonacci, −2, . . .
- Observation. In all these presentations the codes of the numbers in
natural order 0, 1, 2, 3, · · · are ordered in reverse length-lexicographic order.
- Eg. 0, 1, 10, 11, 100, 101, 110, · · ·
SLIDE 7
Space-efficient presentations of +
Basic systems: base 10, base 2, . . . Non-standard systems: Fibonacci, −2, . . .
- Observation. In all these presentations the codes of the numbers in
natural order 0, 1, 2, 3, · · · are ordered in reverse length-lexicographic order.
- Eg. 0, 1, 10, 11, 100, 101, 110, · · ·
- Conjecture. In every space efficient presentation of +