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Iterative Network for Radix Conversion

IP.com Disclosure Number: IPCOM000094823D
Original Publication Date: 1965-Jun-01
Included in the Prior Art Database: 2005-Mar-06
Document File: 2 page(s) / 45K

Publishing Venue

IBM

Related People

Isberg, CA: AUTHOR

Abstract

This iterative network effects radix conversion from binary to tertiary. The representation is in binary notation.

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Iterative Network for Radix Conversion

This iterative network effects radix conversion from binary to tertiary. The representation is in binary notation.

Drawing 1 shows the basic, generalized iterative cell for conversion C, modulo k to modulo k'. Such conversion is of a number A by repetitive divisions by B, modulo k', to form successive quotients A, modulo k, and successive remainders B', modulo k'. The latter comprise the orders of the new number. The least significant digit is formed first. The most significant digit is formed when the quotient is reduced to zero.

Drawing 2 is a truth table corresponding to the conversion of a number from k = 2 to k' = 3. Since representation is binary, B and B' each comprise a pair of signals B1 and B2 to form their ternary value.

Drawing 3 shows the block circuitry for this conversion; the same network is iterated in each of the cells. A horizontal row of cells performs one division of the conversion, forming one digit of the ternary number. Such a row also forms remainders, modulo 2, which are similarly treated by the next lower row of cells. When the remainder is reduced to zero, conversion is complete. The logic within the iterative cell can be derived from drawing 2. A' = A(B(1)B(2) + B(1)B(2))

B(1)' = AB(1)B(2) + AB(1)B(2)

B(2)' = B(2)(AB(1) + AB(1))

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