math

• sum

  • awk

  • datamash

  • bc

  • jq

  • $(())

• sum from file

• number conversion

  • Common Bases

  • binary <> decimal <> hexadecimal

  • to decimal

  • to hexadecimal

  • to octal

  • to binary

  • to unicode ( hexadecimal )

  • number converting from file

• advanced computing

  • logarithm

  • power

  • square

[!NOTE|label:references:]

• Bash 的算术运算
• Linux 中bc命令实现自然对数、指数运算、自然指数、平方根的运算
• bc to Perform Advanced Arithmetic Operations in BASH
• Using vim as calculator

sum

[!INFO|label:references:]

• Shell command to sum integers, one per line?
• Summing a List of Numbers

awk

$ seq 10 | awk '{s+=$1} END {print s}'
55

# or
$ awk 'BEGIN{print '"1+2+3"'}'
6

file sizes

$ ls -l
total 12
-rw-r--r--  1 marslo staff 3480 Dec 21 21:21 README.md
-rw-r--r--  1 marslo staff 7516 Dec 21 21:21 SUMMARY.md
drwxr-xr-x  7 marslo staff  224 Sep 19 19:52 artifactory
drwxr-xr-x 15 marslo staff  480 Dec 21 21:19 cheatsheet
drwxr-xr-x 12 marslo staff  384 Aug 17 21:11 devops
drwxr-xr-x  9 marslo staff  288 Sep 29 17:31 jenkins
drwxr-xr-x 10 marslo staff  320 Sep 19 19:52 linux
drwxr-xr-x  9 marslo staff  288 Sep 19 19:52 osx
drwxr-xr-x  6 marslo staff  192 Aug 17 21:11 programming
drwxr-xr-x 27 marslo staff  864 Aug 17 22:10 screenshot
drwxr-xr-x  7 marslo staff  224 Oct 11 19:41 tools
drwxr-xr-x  8 marslo staff  256 Aug 30 16:39 vim
drwxr-xr-x  5 marslo staff  160 Aug 17 21:11 virtualization

$ ls -l | awk '{sum += $5} END {print sum}'
14676

datamash

[!TIP|label:reference:]

• Shell command to sum integers, one per line?

$ seq 10 | datamash sum 1
55

bc

• paste + bc

  $ seq 10 | paste -sd+ -
  1+2+3+4+5+6+7+8+9+10
  
  $ seq 10 | paste -sd+ - | bc
  55

• xargs + bc

  $ seq 10 | xargs printf "- - %s" | xargs | bc
  55

• sed + bc

  $ seq 10 | sed 's/^/.+/' | bc
  1
  3
  6
  10
  15
  21
  28
  36
  45
  55

jq

$ seq 10 | jq -s 'add'
55

$(())

$ f=$(seq 10)
$ echo $(( ${f//$'\n'/+} ))
55

# or
$ echo $(( $(seq 10 | tr "\n" "+") 0 ))
55
# or from file
$ echo $(( $( tr "\n" "+"  < /tmp/test) 0 ))

sum from file

[!NOTE|label:sample file:]

$ cat numbers.txt
73.27
218.38
14.15
9.18
16.60

• How can I quickly sum all numbers in a file?

• awk

  
  $ awk '{ sum += $1 } END { print sum }' numbers.txt
  331.58

• paste && bc

  $ paste -sd+ numbers.txt
  73.27+218.38+14.15+9.18+16.60
  
  $ paste -sd+ numbers.txt | bc
  331.58

  • Σn where 1<=n<=100000

    $ seq 100000 | paste -sd+ | bc -l
    5000050000

• jq

  $ paste -sd' ' numbers.txt | jq -s add
  331.58

number conversion

[!NOTE|label:references:]

• Understand "ibase" and "obase" in case of conversions with bc?
• Linux / UNIX: bc Convert Octal To Hexadecimal or Vise Versa
• tips

ibase and obase params order matters, but not always. Hex values must be in UPPERCASE.

• the decimal can be ignored in ibase or obase, or we can say, the default ibase and obase are all 10.

CONVERT	IN BC	OUTPUT
八进制 → 二进制	echo "ibase=8; obase=2; 77" | bc	111111
十进制 → 十六进制	echo "obase=16; 255" | bc	FF
十六进制 → 十进制	echo "ibase=16; FF" | bc	255
二进制 → 十进制	echo "ibase=2; 101010" | bc	42

#!/usr/bin/env bash

function convertBase() {
  local from_base=''
  local to_base=''
  local value=''
  local upper=false

  while [[ $# -gt 0 ]]; do
    case "$1" in
      -f|--from  ) from_base="$2" ;  shift 2 ;;
      -t|--to    ) to_base="$2"   ;  shift 2 ;;
      -v|--value ) value="$2"     ;  shift 2 ;;
      -u|--upper ) upper=true     ;  shift   ;; # uppercase hex
      -h|--help  ) echo "Usage: convertBase -f <from_base> -t <to_base> -v <value> [-u]"
                   echo "Supported bases: bin, dec, oct, hex"
                   return 0
                   ;;
      *          ) echo "Unknown option: $1" >&2; return 1 ;;
    esac
  done

  # Map base names to numeric bases for bc
  declare -A base_map=(
    [bin]=2
    [oct]=8
    [dec]=10
    [hex]=16
  )

  local ibase="${base_map[$from_base]}"
  local obase="${base_map[$to_base]}"

  if [[ -z "$ibase" || -z "$obase" ]]; then
    echo "Error: Unsupported base. Use bin, dec, oct, hex." >&2
    return 1
  fi

  # For hex input, force uppercase since bc expects that
  if [[ "$from_base" == "hex" ]]; then
    value="${value^^}"
  fi

  # Use bc to convert
  result=$(echo "obase=$obase; ibase=$ibase; $value" | bc)

  # Format output (uppercase optional)
  if [[ "$upper" == true && "$to_base" == "hex" ]]; then
    result="${result^^}"
  fi

  echo "$result"
}

# usage
$ convertBase -f hex -t dec -v FF         # → 255
$ convertBase -f bin -t dec -v 1011       # → 11
$ convertBase -f dec -t hex -v 255        # → ff
$ convertBase -f dec -t hex -v 255 -u     # → FF
$ convertBase -f dec -t bin -v 42         # → 101010
$ convertBase -f oct -t hex -v 77         # → 3F
$ convertBase -f bin -t oct -v 110101     # → 65

• supported base keywords

NAME	BASE	DESCRIPTION
bin	2	Binary
oct	8	Octal
dec	10	Decimal
hex	16	Hexadecimal

Common Bases

CONVERSION TYPE	TOOL / METHOD	EXAMPLE
Base → Decimal	$((base#value))	echo $((2#1010)) → 10
Decimal → Hex	printf	printf "%X\n" 255 → FF
Decimal → Binary	bc	bc < <(echo "obase=2; 42") → 101010
Octal → Decimal	$((8#17)) $((017))	echo $((8#17)) → 15
Hex → Decimal	$((16#FF)) $((0xFF))	echo $((16#FF)) → 255

• base → decimal

BASE	TO	SYNTAX	INTERPRETED NUMBER	OUTPUT (DECIMAL)	DESCRIPTION
2	10	$((2#1011))	1011	11	BINARY
8	10	$((8#17))	17	15	OCTAL
8	10	$((017))	17	15	OCTAL
10	10	$((10#42))	42	42	DECIMAL
16	10	$((16#1A3F))	1A3F	6719	HEXADECIMAL
16	10	$((0x1A3F))	1A3F	6719	HEXADECIMAL
36	10	$((36#Z))	Z	35	ALPHANUMERIC MAX
64	10	$((64#_))	_	63	MAX BASE IN BASH

binary <> decimal <> hexadecimal

[!NOTE]

• obase : [o]utput base

• ibase : [i]utput base

# bin -> dec
$ bc <<< 'ibase=2;11111111;11111111;11000000;00000000' | paste -sd. -
255.255.192.0

# bin -> hex
$ bc <<< 'obase=16;ibase=2;11111111;11111111;11000000;00000000' | awk '{ printf "%04s\n", $1 }' | paste -sd. -
00FF.00FF.00C0.0000

# dec -> bin
$ bc <<< 'ibase=10;obase=2;255;255;240;0' | numfmt --format %08f | paste -sd' ' -
11111111 11111111 11110000 00000000

# dec -> hex
$ bc <<< 'ibase=10;obase=16;255;255;240;0' | awk '{ printf "%04s\n", $1 }' | paste -sd. -
00FF.00FF.00F0.0000

# hex -> bin
$ bc <<< 'ibase=16;obase=2;FF;FF;EE;0A' | numfmt --format %08f | paste -sd' ' -
11111111 11111111 11101110 00001010

# hex -> dec
$ bc <<< 'ibase=16;FF;FF;EE;0A' | paste -sd. -
255.255.238.10

to decimal

FROM	TO	COMMAND (BASH)	EXAMPLE	OUTPUT	COMMENT
Binary	Decimal	echo $((2#1010))	2#1010	10	-
Hex	Decimal	echo $((16#FF))	16#FF	255	-
Hex	Decimal	echo $((0xFF))	16#FF	255	0x - convert from hex
Octal	Decimal	echo $((8#77))	8#77	63	-
Octal	Decimal	echo $((077))	8#77	63	0 - convert from octal

• from hexadecimal

  $ echo "ibase=16; F" | bc
  15
  
  # [o]utput base:       0xA -> 10
  #                       ^
  $ echo "ibase=16; obase=A; F" | bc
  15
  
  # or obase first
  $ echo "obase=10; ibase=16; F" | bc
  15
  
  # or
  $ echo $((0xF))
  15

• from octal

  # obase (decimal) first
  $ echo "obase=10; ibase=8; 17" | bc
  15
  
  # or
  #                     ╭─ 012 -> 10
  #                     --
  $ echo "ibase=8;obase=12; 17" | bc
  15
  
  # or
  $ echo $((017))
  15

to hexadecimal

[!TIP]

• if convert from decimal, the ibase can be ignored, or we can say, the default ibase is 10.

FROM	TO	COMMAND	EXAMPLE	OUTPUT
Binary	Hex	echo "obase=16; ibase=2; 101011" | bc	101011 → hex	2B
Octal	Hex	echo "obase=16; ibase=8; 77" | bc	77 (octal) → hex	3F
Decimal	Hex	echo "obase=16; 255" | bc	255	FF
Decimal	Hex	printf "%X\n" 255	255	FF

• from decimal

  $ echo "obase=16; 15" | bc
  F
  
  # or
  $ echo "ibase=10;obase=16; 15" | bc
  F

• from octal

  $ echo "obase=16; ibase=8; 17" | bc
  F
  
  # or
  $ printf "%x\n" 017
  f

to octal

FROM	TO	COMMAND	EXAMPLE	OUTPUT
Binary	Octal	echo "obase=8; ibase=2; 1010" | bc	1010 → base 2 → base 8	12
Decimal	Octal	printf "%o\n" 42	42	52
Hex	Octal	echo "obase=8; ibase=16; FF" | bc	FF → hex to octal	377

• from hexadecimal

  $ echo "ibase=16;obase=8; F" | bc
  17

• from decimal

  $ echo "obase=8; 15" | bc
  17
  
  # or
  $ echo "ibase=10;obase=8; 15" | bc
  17

to binary

[!NOTE|label:references:]

• Prevent bc from auto truncating leading zeros when converting from hex to binary
• How to make bc output a desired number of base-2 binary digits

FROM	TO	COMMAND	EXAMPLE	OUTPUT
Octal	Binary	echo "obase=2; ibase=8; 77" | bc	8#77 → obase=2	111111
Decimal	Binary	echo "obase=2; 42" | bc`	42	101010
Hex	Binary	echo "obase=2; ibase=16; FF" | bc	ibase=16; FF → obase=2	11111111

• from decimal

  $ bc <<< 'obase=2;15'
  1111
  
  $ bc -l <<< 'obase=2;0;0;15;255' | xargs
  0 0 1111 11111111
  
  $ bc -l <<< 'obase=2;0;0;15;255' | awk '{ printf "%08d\n", $0 }' | xargs
  00000000 00000000 00001111 11111111
  
  $ printf "%08d\n" $(echo "obase=2; 0;0;15;255" | bc) | xargs
  00000000 00000000 00001111 11111111
  
  $ bc <<< 'obase=2; 0;0;15;255' | numfmt --format=%08f | xargs
  00000000 00000000 00001111 11111111

to unicode ( hexadecimal )

[!NOTE|label:references:]

• Convert a character from and to its decimal, binary, octal, or hexadecimal representations in BASH / Shell

# 0x41 -> `A`; 0x61 -> `a`

# decimal -> hexadecimal
$ printf "$(printf %04x 65)\n"
0041

# \u<4-digits-hex>
$ printf "\u$(printf %04x 65)\n"
A

# \U<8-digits-hex>
$ printf "\U$(printf %08x 67147)\n"
𐙋

$ single_unicode_char="😈"
$ printf %d "'$single_unicode_char"
128520
$ printf "$(printf %08x 128520)\n"
0001f608
$ printf "\U$(printf %08x 128520)\n"
😈

• more

  $ single_unicode_char="😈"

• to hexadecimal

  #         ╭─ hexadecimal
  $ printf %x "'$single_unicode_char'"
  1f608
  $ printf %08X "'$single_unicode_char'"
  0001F608
  #                                                               ╭─ hexadecimal
  $ echo -n $single_unicode_char | iconv -t UTF-32LE | od -A n -t x4
   0001f608
  $ printf "\U0001f608"
  😈
  
  # or
  $ printf %#x "'$single_unicode_char"
  0x1f608
  $ printf %#X "'$single_unicode_char"
  0X1F608
  $ printf "\U$(printf %08x 0X1F608)\n"
  😈
  
  # or
  #                                           ╭─ hexadecimal
  $ echo -n $single_unicode_char | od -A n -t x1
   f0 9f 98 88
  $ printf %b "\xf0\x9f\x98\x88"
  😈
  #       ╭─ works without `%b` as well
  $ printf "\xf0\x9f\x98\x88"
  😈

• to octal

  #         ╭─ octal
  $ printf %o "'$single_unicode_char'"
  373010
  #                                                               ╭─ octal
  $ echo -n $single_unicode_char | iconv -t UTF-32LE | od -A n -t o4
   00000373010
  $ printf "\U$(printf %08x "00000373010")"
  😈
  
  # or
  #       ╭─ without `\n`
  $ echo -n $single_unicode_char | od -A n -t o1
   360 237 230 210
  $ printf %b "\360\237\230\210"
  😈

number converting from file

• octal

  $ cat -p octal-data-file.txt
  7
  10
  11
  12
  13
  14
  15
  16
  17
  20
  21
  
  # octal -> hexadecimal
  $ ( echo "obase=16; ibase=8" ; cat octal-data-file.txt ) | bc
  7
  8
  9
  A
  B
  C
  D
  E
  F
  10
  11
  
  # octal -> decimal
  $ ( echo "obase=10; ibase=8" ; cat octal-data-file.txt ) | bc
  7
  8
  9
  10
  11
  12
  13
  14
  15
  16
  17

• hexadecimal

  $ cat -pp hex-data-file.txt
  9
  A
  B
  C
  D
  E
  F
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  1A
  1B
  1C
  1D
  1E
  1F
  20
  
  # hexadecimal -> octal
  $ ( echo "obase=8; ibase=16" ; cat hex-data-file.txt ) | bc
  11
  12
  13
  14
  15
  16
  17
  20
  21
  22
  23
  24
  25
  26
  27
  30
  31
  32
  33
  34
  35
  36
  37
  40
  
  # hexadecimal -> decimal
  $ ( echo "obase=10; ibase=16" ; cat hex-data-file.txt ) | bc
  9
  10
  11
  12
  13
  14
  15
  16
  17
  18
  19
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32

advanced computing

[!NOTE|label:references:]

• How to calculate the log of a number using bc?
• 指数与对数
• n次方根

logarithm

• bc

  $ bc -l <<< 'l(9)/l(3)'
  2.00000000000000000000

  • 🫠

    $ bc -l <<< 'l(512)/l(2)'
    9.00000000000000000008

• awk

  $ echo 512 | awk '{print log($1)/log(2)}'
  9

power

• bc

  $ bc <<< '2^3'
  8

• $(())

  $ echo $(( 2**8 ))
  256

square

$ bc -l <<< 'sqrt(2)'
1.41421356237309504880

$ bc <<< 'sqrt(2)'
1