By Fomin A.A.
Each τ -adic matrix represents either a quotient divisible workforce and a torsion-free, finite-rank workforce. those representations are an equivalence and a duality of different types, respectively.
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Additional info for A category of matrices representing two categories of Abelian groups
Examples 1. Shift the accumulator right 1 bit arithmetically, preserving the sign (most significant) bit. TAX ASL TXA A ROR A ;SAVE THE ACCUMULATOR ;MOVE BIT 7 TO CARRY ;RESTORE THE ACCUMULATOR ;SHIFT THE ACCUMULATOR, COPYING BIT 7 When the processor performs ROR A, it moves the Carry (the old bit 7) to bit 7 and bit 7 to bit 6, thus preserving the sign of the original number. 2. Shift the accumulator left 1 bit arithmetically, preserving the sign (most sig nificant) bit. ASL A ROL A ;SHIFT A, MOVING BIT 7 TO CARRY ;SAVE BIT 7 IN POSITION 0 A ;CHANGE ROR A ;SHIFT THE ASL A CLRSGN #%10000000 ;SHIFT A, MOVING BIT ;WAS BIT 7 1?
Branch to DEST if bit 2 of the accumulator is 0. AND #%00000100 BEQ DEST ;TEST BIT 2 OF A There are special short procedures for examining bit positions 0, 6, or 7. Bit 7 is available readily as the Negative flag after a Load or Transfer instruction; bit 0 can be moved to the Carry with LSR A or ROR A; bit 6 can be moved to the Negative flag with ASL A or ROL A. 3. Branch to DEST if bit 7 of memory location ADDR is 1. LDA BMI ADDR DEST ;IS BIT 7 1? ;YESf BRANCH Note that LDA affects the Zero and Negative flags; so do transfer instructions such as TAX, TYA, TSX (but not TXS), and PLA.
Handling one character at a time is just like handling normal 8-bit unsigned numbers. Some examples are • Branch to address DEST if the accumulator contains an ASCII E. CMP #'E ;IS BEQ DEST ;YES, DATA E? BRANCH • Search a string starting at address STRNG until a non-blank character is found. EXAMC LDX LDA CMP #0 #■ STRNG,X ;POINT TO START OF STRING ;GET A BLANK FOR CHECKING ;IS NEXT CHARACTER A BLANK? DONE ;NO, DONE ;YES,PROCEED TO NEXT CHARACTER DONE BNE INX JMP NOP LDX LDA #$FF #' ;POINT TO BYTE BEFORE START ;GET A BLANK FOR COMPARISON INX CMP STRNG,X ;PROCEED TO NEXT ;IS IT A BLANK?
A category of matrices representing two categories of Abelian groups by Fomin A.A.