These operators convert between decimal and another number base. The code originates from the PPC ROM Module released by the international group People Programming Computers on December 1981 [1,2].
Instructions
Use XEQ “DB” for base 10 to base b with b in the range [2,19]. DB takes its base 10 input from the Xregister. The result is returned in the alpha register.
Use XEQ “BD” for base b to base 10 with base b in the range [2,25]. The input is through the alpha register. The result is returned in the X register.
Listing
Available through the repository

Requires
 XFunctions module on the HP41cv

Available as
 source code
 raw code for the V41 emulator
 bar code for the HP Wand (HP82153A)

Note
 Register 06 is used to store the base.
; BASE TO DECIMAL 01 LBL "BD" 02 XEQ 06 ; input base 03 AON 04 STOP ; input number 05 AOFF ; prepare for main loop 06 CLST ; X=0, Z=0, T=0 07 LBL 01 ; base 10 number will accumulate in Y register 08 >"+" ; append blanks in alpha until the first character 09 X<> O ; of the alpha input is pushed into alpha char 10 X=0? ; 1521 (O register). 12 X<> M ; In the loop, the next char which appears in O is 13 R^ ; exchanged with M and the stack is rolled up to 14 X<> N ; preserve M in the stack. The N register is then 15 "\00\08" ; bought into X and O is stored in N. The alpha 16 X<> N ; register (MNO) now contains only the net character. 17 RDN ; 0x0008 is appended. N is then returned with its 18 X<> M ; original content, the stack is rolled down and then 19 E ; the M register is restored and our next character 20 * ; now appears as a decimal number in X. This number 21 39 ; is multiplied by 1 so it becomes normalized and then 22  ; 39 is subtracted so we may test whether our char is 23 X>0? ; a digit 09 (row 3 in the next table) or a letter 24 DSE X ; (row 4). The X register is then transformed to its 25 9 ; true decimal value. 26 + ; It is then tested to see if it is a valid number 27 X<0? ; (a blank would yield a negative at this point 28 GTO 02 ; causing a jump to LBL 02). 29 X<>Y ; If not a blank, the accumulated result is multiplied 30 RCL 06 ; by the base and the next digit is added. 31 * 32 + 33 . ; Ensure the Y register is the only nonzero stack 34 GTO 01 ; register when the jump is made back to LBL 01. 35 LBL 02 ; End the routine by rolling down the stack to bring 36 RDN ; the Y register result into X and the alpha register 37 CLA ; is cleared. 38 RTN ; DECIMAL TO BASE 39 LBL "DB" 40 XEQ 06 ; input base 41 STOP ; input number 42 "\27 " ; single quote followed by 13 spaces 43 RCL M ; Recall 7 spaces into the stack. These blanks float 44 X<>Y ; up and down in the stack throughout the main loop 45 LBL 03 ; and are not used until line 74. 46 ENTER^ ; The main loop. At the start the remaining base 10 47 INT ; number is in X and the 7 spaces in Y. The base b 48 RCL 06 ; digits are built up starting with the least 49 MOD ; significant digits. The base 10 equivalent is 50 9 ; computed at lines 4849. Lines 5057 convert this 51  ; decimal number to its alpha equivalent stored in O. 52 X>0? 53 ISG X 54 LBL 04 55 39 56 + 57 10^X 58 STO O ; Line 58 acts as an append to the remaining char in 59 >" " ; alpha. The next 4 lines do an alpha shift to 60 CLX ; prepare M and N for the next char (digit) to be 61 X<> O ; appended. 62 X<> N 63 STO M 64 RDN ; Calculate the remaining base 10 result and branch 65 RCL 06 ; to LBL 03 as long as this number is nonzero. 66 / 67 INT 68 X#0? 69 GTO 03 70 LBL 05 ; Pad space char in alpha so the result is left 71 >" " ; justified. 72 CLX 73 RCL M 74 X#Y? ; Comparison test with the 7 spaces. 75 GTO 05 76 CLX ; Alpha shift so that the final digits are in M 77 X<> O ; and N 78 X<> N 79 STO M 80 CLST ; Finish by clearing the stack view in the alpha 81 AVIEW 82 RTN 83 LBL 06 84 "BASE ?" 85 PROMPT 86 STO 06 87 "SOURCE ?" 88 AVIEW 89 RTN 90 END
References
[1]  BD – BASE b TO BASE DECIMAL George Eldridge and John Kennedy, August 1981 PPC ROM Users Manual, pg.5253  
[2]  TB – BASE 10 TO BASE b George Eldridge and John Kennedy, August 1981 PPC ROM Users Manual, pg.430431 