A320 CREW AFTER PUSHBACK SFO ARE ADVISED DEPARTING RWY CHANGED FROM RWY 1L TO RWY 10L AND WHILE TAXIING CROSS RWY 10R WITHOUT CLRNC.

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AFTER PUSHBACK IN SFO; THE DEPARTING RWY CHANGED FROM RWY 1L TO RWY 10L. GND CTL CLRED US TO TAXI FROM ABEAM GATE XX TO RWY 10R VIA TXWY B AND TXWY U. I ASKED THE CAPT IF HE UNDERSTOOD THE INSTRUCTIONS AND HE ACKNOWLEDGED. AS WE TAXIED E ON TXWY B; I TOLD THE CAPT THAT I WOULD BE 'HEADS DOWN' WHILE I MADE THE REQUIRED CHANGES TO THE FMGC AND CALCULATED THE PERFORMANCE FOR THE NEW RWY. WHILE STILL ON TXWY B; GND TOLD US TO GIVE WAY TO AN ACR Y JET TURNING ON TXWY U FROM TXWY B AND HE WOULD BE OUR SEQUENCE. I ACKNOWLEDGED THE CALL AND CONFIRMED THE CAPT UNDERSTOOD. I TOLD THE CAPT I WOULD BE HEADS DOWN AGAIN TO FINISH THE CHANGES FOR THE NEW RWY. WHILE STILL HEADS DOWN; GND CTL INFORMED US THAT WE HAD CROSSED RWY 10R WITHOUT PERMISSION. A VERY SHORT TAXI DISTANCE COMBINED WITH A HIGH WORKLOAD ON MY PART LEFT LITTLE TIME FOR ME TO BACK UP THE CAPT WHILE HE TAXIED. GIVEN A SIMILAR SIT; I WOULD TRY TO VARY THE TIME FROM HEADS UP TO HEADS DOWN TO BETTER BACK UP THE CAPT DURING TAXI OR WAIT UNTIL THE ACFT IS STOPPED TO MAKE REQUIRED CHANGES.