Question

Multiply in octal using refined hardware 72 x 23

Divide in hex using refined hardware 54 by 12

Answer 1

Multiply in Octal using refined hardware 72 X 23:

In an octal number system, base or radix is equal to 8 i.e r = 8 so we have 0 to 7 different digits, now 3 x 7 = 21 which is not an octal number so we have to break 21 = 2 x 8 + 5 then 5 will be taken and 2 will be the carry on for next step so finally 2 5 6 will be found, now for the next step also 2 x 7 = 14 which is again not an octal number so we have to break 14 = 1 x 8 + 6, here 6 will be taken and 1 will be carried on so final 1 2 4 is found, finally need to the addition of number which will be the final answer, on the second line 9 is not an octal number so 9 = 1 x 8 + 1, 1 will be taken and 1 will carry on the same way for the next step and so on, the final answer will be 1 5 1 6.

The hexadecimal number system has got 16 digits that is 0-9 and A-F so,

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F where A = 11, B = 12, C = 13, D = 14, E = 15, F = 16

hexadecimal numbers are positon value system.

The value of quotient and reminder based on Hexadecimal Multiplication table, where 6 to C.