• https://tldp.org/LDP/abs/html/dblparens.html

انجام ساده تر محاسبات ریاضی

#!/bin/bash
# c-vars.sh
# Manipulating a variable, C-style, using the (( ... )) construct.
 
echo +==========================================+
 
(( a = 23 ))  #  Setting a value, C-style,
              #+ with spaces on both sides of the "=".
echo "a (initial value) = $a"   # 23
 
(( a++ ))     #  Post-increment 'a', C-style.
echo "a (after a++) = $a"       # 24
 
(( a-- ))     #  Post-decrement 'a', C-style.
echo "a (after a--) = $a"       # 23
 
 
(( ++a ))     #  Pre-increment 'a', C-style.
echo "a (after ++a) = $a"       # 24
 
(( --a ))     #  Pre-decrement 'a', C-style.
echo "a (after --a) = $a"       # 23
 
echo +==========================================+
#  Like C, pre- and post-decrement operators
#+ have different side-effects.
 
n=1
(( --n )) && echo "True" || echo "False"  # False
 
n=1
(( n-- )) && echo "True" || echo "False"  # True
 
echo +==========================================+
# C-style ternary operator.
(( t = a<45?7:11 ))   
#       ^  ^ ^
echo "If a < 45, then t = 7, else t = 11."  # a = 23
echo "t = $t "                              # t = 7
 
echo +==========================================+
# Using C-like syntax.
LIMIT=10
for ((a=1; a <= LIMIT ; a++))  # Double parentheses, and naked "LIMIT"
do
  echo -n "$a "
done                           # A construct borrowed from ksh93.
echo
 
echo +==========================================+
# Let's use the C "comma operator" to increment two variables simultaneously.
LIMIT=10
for ((a=1, b=1; a <= LIMIT ; a++, b++))
do  # The comma concatenates operations.
  echo -n "$a-$b "
done
 
exit

• https://tldp.org/LDP/abs/html/numerical-constants.html

ثوابت عددی و تبدیل مبنا

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).

#!/bin/bash
# numbers.sh: Representation of numbers in different bases.
 
# Decimal: the default
let "a = 32"
echo "decimal number = $a"              # 32
# Nothing out of the ordinary here.
 
 
# Octal: numbers preceded by '0' (zero)
let "a = 032"
echo "octal number = $a"                # 26
# Expresses result in decimal.
# --------- ------ -- -------
 
 
# Hexadecimal: numbers preceded by '0x' or '0X'
let "a = 0x32"
echo "hexadecimal number = $a"          # 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 "a = 2#111100111001101"
echo "binary number = $a"               # 31181
 
let "a = 32#77"
echo "base-32 number = $a"              # 231
 
let "a = 64#@_"
echo "base-64 number = $a"              # 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)) $((64#__7@))
                                         # 1295 170 44822 3375 16773630