math

[!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

$ 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

十六进制 → 十进制

echo "ibase=16; FF" | bc

255

二进制 → 十进制

echo "ibase=2; 101010" | bc

#!/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

Binary

oct

Octal

dec

Decimal

hex

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

SYNTAX

INTERPRETED NUMBER

OUTPUT (DECIMAL)

DESCRIPTION

$((2#1011))

1011

11

BINARY

$((8#17))

17

15

OCTAL

$((017))

17

15

OCTAL

$((10#42))

42

DECIMAL

$((16#1A3F))

1A3F

6719

HEXADECIMAL

$((0x1A3F))

1A3F

6719

HEXADECIMAL

$((36#Z))

Z

35

ALPHANUMERIC MAX

$((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

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

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

COMMAND

EXAMPLE

OUTPUT

Binary

Octal

echo "obase=8; ibase=2; 1010" | bc

1010 → base 2 → base 8

12

Decimal

Octal

printf "%o\n" 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

COMMAND

EXAMPLE

OUTPUT

Octal

Binary

echo "obase=2; ibase=8; 77" | bc

8#77 → obase=2

111111

Decimal

Binary

echo "obase=2; 42" | bc`

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 -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

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