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Q: How much power does the rex use?
A few users have made measurements which broadly agreed with each other:
On, steady ->3 to 4 mA
Processor operating ->7 mA
Writing on EEPROM peaks of -> 7.5 to 10mA
Extended flash writes/erases (such as when updating entire 64KB sectors of flash memory) could draw as much as 30 mA. - measured during delete operations in Adder app.

The speaker seems to draw only .5 mA
It does not matter what the Rex6000 is doing: drawing the world clock, getting key taps from the soft keyboard, switching from one calendar day to another and searching for dates - all jobs need the same power

Q: What chips are used?
Memory: The data sheet for the flash memory chips used in Rex (4 x Fujitsu 29DL164BD-90) is on Fujitsu's site.
Each of the 2 Fujitsu MBM 29DL164BD chips in the Rex is 16 Mb; 16Mbits in the chip is accessible as two banks of 8Mbits. With 8bits per byte, this means each chip is 2MB, accessible as two banks of 1MB. Times two chips gives a total of 4MB flash memory in the Rex.
Database: The Fujitsu "SoFFS" (Sophisticated Flash File System) seems to be the basis of Rex's database filesystem, just look at the database.h:
#define DB_ERR_SOFFS -13
It seems that Citizen added a complete database layer on top of SOFFS, in order to encapsulate and hide SOFFS functionality. SoFFS is apparently provided only to OEMs who buy the chips, but there is a catalog

Processor Toshiba T6B31 running z80 code

Realtime clock is a TC8521, which appears to match the descriptions in z80.h. View the datasheet

LCD column & row drivers the T6A39 and T6A40.