Trouble making mathematical operations with big hexadecimal numbers on bash

Question

I'm trying to perform multiple mathematical operations with big hexadecimal numbers. In the following code a big random value is given to p and q , both variables are multiplied together making the result the value of n . Then make a subtraction " (n-2) " but when subtracting 2 to n the result seems like being wrong

#!/bin/bash

generate_random() {

        head -c 256 /dev/urandom | xxd -p -u -c 256 | tr -d '[:space:]\\'
}

p="$(generate_random)"
q="$(generate_random)"

n=$(echo "${p} * ${q}" | tr -d '[:space:]\\')

echo "obase=16; ${n} - 2" | bc | tr -d '[:space:]]\\'

I'm using this webstie to check the results and so far I haven't managed to get any correct output from my script

Value examples:

Generated value for p

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

Generated value for q

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

Result of n

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

Expected value for n

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

Answer 1

Since the input is in hexadecimal you should also use ibase.

#!/bin/bash

generate_random() {

        head -c 256 /dev/urandom | xxd -p -u -c 256 | tr -d '[:space:]\\'
}

p="$(generate_random)"
q="$(generate_random)"

n=$(echo "${p} * ${q}" | tr -d '[:space:]\\')

echo "obase=16;ibase=16; ${n} - 2" | bc | tr -d '[:space:]]\\'

The result in the case you posted is -

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

This can be confirmed using python

In [1]: hex(0x28DA11279C9BF6B6A93CF1288C63845503D87C17C93554421C3069A5283547CEE4C127F3289BDC03663143808B7318B321B35B25ECC6D48EF60283DA6111104291070E3FBEDBD27A942D2B3630AA8683C6BB4F6F6EE277A24A4C9B93AEEB61D48AC7657F
   ...: A6E61DC95A8EF133F97C6ED3B285E275487746F070005B2BCDEA9C7C12F294DFCE55BC7013417F8E47CEC605F13AFD5C54A3578BB041278285511248E975FE29F4013CA059599EE95E43E28B886D0651EFDDFF760DBB298096C7CA1A46FE3D119914C23ABA5543
   ...: C43BE546FA70D7FA36B22DA17210A6CABDCD299751ADEE381A3230E9978946B193AB02921947887A2FC7A5DC84D2193F9CFC865B52*0x54DEBA70F8F052F5120B77254EB999E12180241520DC2A12F62F6773992155AEFC5356E3F9B3271FE5AA9D425F7D2CD82
   ...: 33196C98595F993899C31D4063F75A801D1752AD178663E3CDF3CF38CEE1972C861DC6069B787249963D305E4FC970A48E67D3A680CD58F17229379EAE5445603E50E60CF605F1057766EFEAFAA2299CCBC0C4F161815DBD06294E4BBD43EF55F1E2D7544B3927
   ...: 9EA4B9114AB9F9D0FC2B46135911CF62FB4A22A615936FDDAD23131B1F0AD2FB94D44C0879B3289530653C4714B2E3F3F9FFD17E92C44FBCE589982F68985207F788FBD1B531C56224E4EDA1F124E6AEC19C949AB396862F0856C435EBAAAB7FFB1251FBEB3386
   ...: 76D-2)
Out[1]: '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'

Not sure what is the calculator you're using but it has a different calculation for some reason.