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## Topic: FOCUS number system

topics > computer science > data > Group: data value

Topic:
builtin functions
Topic:
integer values and operations
Topic:
kinds of numbers
Topic:
numerical error
Topic:
real numbers and floating point numbers
Topic:
unbounded precision

#### Summary

FOCUS numbers from a logarithmic system with unity mantissa. Since all information is carried by the exponent, multiplication and division is exact. Addition and subtraction requires a table lookup. Multiplication by a constant is the fastest operation. Zero doesn't exist. Its main advantages are speed of operation and efficiency of representation. A 16-bit FOCUS system performs 3 times faster than 8-bit arithmetic (using a representative mix of add, subtract, multiple, and divide), but has the performance of an 18-bit floating point system. (cbb 5/80)
Subtopic: FOCUS -- logarithmic numbers

 Quote: FOCUS use logarithmic numbers with fractional exponents and no mantissa [»edgaAD3_1979] Quote: 8-bit FOCUS numbers nearly represent the range covered by 16-bit fixed point words [»edgaAD3_1979] Quote: FOCUS addition and subtraction uses a lookup table; 2K for 16-bit system [»edgaAD3_1979] Quote: FOCUS does not have a zero, but this is not needed in control systems except for counting [»edgaAD3_1979]

Subtopic: performance

 Quote: in FOCUS, multiplication and division are fastest and invoke no roundoff error; by a constant is one instruction [»edgaAD3_1979] Quote: 16-bit FOCUS routines run faster than 8-bit fixed point; similar to 18-bit floating point [»edgaAD3_1979] Quote: 8-bit FOCUS executes 5 times faster than an uniform mixture of add, subtract, multiple, and divide [»edgaAD3_1979]

Subtopic: alternatives

 Quote: use i*j/k for efficient calibration, scaling, and rational approximation; e.g., multiply by pi with an error of 10^-7 [»rathED_1996]

Related Topics

Topic: builtin functions (6 items)
Topic: integer values and operations (13 items)
Topic: kinds of numbers (24 items)
Topic: numerical error (19 items)
Topic: real numbers and floating point numbers (37 items)
Topic: unbounded precision
(9 items)

Updated barberCB 6/04