Read decimal number

Context

Given an input '123', reading input will populate cells with values [49], [50] and [51] (ASCII codes of 1, 2 and 3). Here, we want to read 123 as a number, and have one unique value [123].
Therefore, we'll have to:

• Read a char
• Convert it to a digit (-48)
• Multiply the previous result by 10, and add the new digit

Initial state

• Memory: 0, 0, 0, 0
• Cursor: first cell
• Input: a decimal number

Process

• Move to second cell (first is for result)
• While a digit is read
• Convert to decimal digit (-48)
• Multiply first cell by 10 and add current digit
• Loop invariant: first cell = current read number (decimal)
• When all chars are read, first cell equals number to read

Code 

>,[
  >++++++[-<-------->]
  remove 48
  +++++++++[-<<[->+>>+<<<]>>>[-<<<+>>>]<]
  add first cell 9 times to second
  <[-<+>]
  add second cell to first (result: first cell * 10 plus second cell)
  ,
  read next char
]<

Code (minified)

>,[>++++++[-<-------->]+++++++++[-<<[->+>>+<<<]>>>[-<<<+>>>]<]<[-<+>],]<

Final state

• Memory: number value (decimal)
• Cursor: first cell
• Input: empty
• Output: unchanged

Example

Live 'Decimal to ASCII' converter: type a number (e.g. 122) to see the corresponding ASCII char in output (e.g. 'z')