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8.2. Numerical Constants

A shell script interprets a number as decimal (base 10), unless that number has a special prefix or notation. A number preceded by a 0 is octal (base 8). A number preceded by 0x is hexadecimal (base 16). A number with an embedded # evaluates as BASE#NUMBER (with range and notational restrictions).

Example 8-4. Representation of numerical constants

#!/bin/bash
# numbers.sh: Representation of numbers in different bases.

# Decimal: the default
let "dec = 32"
echo "decimal number = $dec"             # 32
# Nothing out of the ordinary here.


# Octal: numbers preceded by '0' (zero)
let "oct = 032"
echo "octal number = $oct"               # 26
# Expresses result in decimal.
# --------- ------ -- -------


# Hexadecimal: numbers preceded by '0x' or '0X'
let "hex = 0x32"
echo "hexadecimal number = $hex"         # 50

echo $((0x9abc))                         # 39612
#     ^^      ^^   double-parentheses arithmetic expansion/evaluation
# Expresses result in decimal.



# Other bases: BASE#NUMBER
# BASE between 2 and 64.
# NUMBER must use symbols within the BASE range, see below.


let "bin = 2#111100111001101"
echo "binary number = $bin"              # 31181

let "b32 = 32#77"
echo "base-32 number = $b32"             # 231

let "b64 = 64#@_"
echo "base-64 number = $b64"             # 4031
# This notation only works for a limited range (2 - 64) of ASCII characters.
# 10 digits + 26 lowercase characters + 26 uppercase characters + @ + _


echo

echo $((36#zz)) $((2#10101010)) $((16#AF16)) $((53#1aA))
                                         # 1295 170 44822 3375


#  Important note:
#  --------------
#  Using a digit out of range of the specified base notation
#+ gives an error message.

let "bad_oct = 081"
# (Partial) error message output:
#  bad_oct = 081: value too great for base (error token is "081")
#              Octal numbers use only digits in the range 0 - 7.

exit $?      # Thanks, Rich Bartell and Stephane Chazelas, for clarification.

$ sh numbers.sh
$ echo $?
$ 1

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