Base Number System- Please help

[Ashiya]

Hello, I do not know about base number system. Can you please explain one question with two methods, so I would be able to do all other questions.

Add: 432 (Base 6) + 255 (Base 6).

Method 1: Convert each number into base 10 and perfrom operation and convert result again into BAse 6.

Method 2: Complete the operation in Base 6.

Thanks

 

[Ashiya]

Hi, I have just figured out the method 1 but I am stuck at the end part.

I converted 432 (base 6) to base 10 by
: 4*36 + 3*6+2*1= 164 (base 10)

Then I convert 255(base 6) to 107 (base10).

SO Can I add the two base 10 numbers that is 164 +107 = 271(base 10)

NOW, How do I convert back to Base(6)?????

 

[stapel]

To learn how to convert between different number bases, try here. :wink:

 

[soroban]

\(\displaystyle \text{Hello, Ashiya!}\)

\(\displaystyle \text{I just figured out Method 1, but I am stuck at the end.}\)

\(\displaystyle \text{I converted }432_6\text{ to base-10: }\;4\!\cdot\!36 + 3\!\cdot\!6+ 2\!\cdot\!1\:=\:164\)

\(\displaystyle \text{Then I converted }255_6 \text{ to }107.\)

\(\displaystyle \text{So I add the two base-10 numbers: }\:164 +107 \:=\: 271\) . . Good work!

\(\displaystyle \text{Now how do I convert back to base-6?}\)

\(\displaystyle \text{There is a procedure for this . . .}\)


\(\displaystyle \begin{array}{cccccc}\text{Divide 271 by 6:} & 271 \div 6 &=& 45 & \text{rem. 1} \\ \text{Divide the quotient by 6:} & 45 \div 6 &=& 7 & \text{rem. 3} \\ \text{Divide the quotient by 6:} & 7 \div 6 &=& 1 & \text{rem. 1} \\ \text{Divide the quotient by 6:} & 1 \div 6 &=& 0 & \text{rem. 1} \end{array}\)


\(\displaystyle \text{When the quotient is zero, we stop . . . and read UP the remainders.}\)


\(\displaystyle \text{Therefore: }271_{10} \;=\;1131_6\)

 

[Deleted member 4993]

Hello, I do not know about base number system. Can you please explain one question with two methods, so I would be able to do all other questions.

Add: 432 (Base 6) + 255 (Base 6).

Method 1: Convert each number into base 10 and perfrom operation and convert result again into BAse 6.

Method 2: Complete the operation in Base 6.

Thanks

Method 2

you can add base 6 numbers like base 10 numbers.

In base 6 after five comes 10

then 11, 12, 13, 14, 15 then comes 20 and so on

so in your when we add 5+2 --> 11

write 1 in unit position and carry-over 1

for 10 position you have 3 + 5 + 1(carried over) --> 13

write 3 in ten position and carry-over 1

for 100 position you have 4 + 2 + 1(carried over) --> 11

write 1 in 100 position and carry-over 1

write 1 in 1000 position

So the added number in base 6 is 1131