it doesnt work like that.  Each byte (a single register is one byte) contains 8 bits, giving the byte a value from 0-255, so if within de, d=1, e=0,  de=256.  if it were d=0,e=1, de=1.  The relationship between the two is basically an extension of the second register in the pair, e.  so if d=1 (%00000001), and e=31 (%00011111), de = 256+35=291, (%0000000100011111).  However, when you extract data from memory into a register pair, the order is reversed.
ie.
 ld hl,(data)

data: .db 0,1           ; data byte is 8 bit data

this would load 0 into register l, and 1 into register h.  so hl = 256

however, the following code would correctly load 5 into hl

 ld hl,(data)

data: .dw 5             ; data word is 16 bit data

i hope that solves any problems with understanding register pairs.