Convert 660677 n8 Convert 2403115 n16 Convert 23615119 n

Convert 66067_7 =>n_8 = Convert 240311_5 => n_16 = Convert 2361511_9 => n_16 = By matching convert the below binary number to the base 8: 1 1 0 1 10 1 10 1 1 10 1 1 10 11 0 1 11.00 11 0 10 10 1 1_2 => n_8 =

Solution

Okay so convert the numbers from one standard to another we first need to convert the standard to the decimal format that is the base 10 format, so to convert a format in decimal form first we need to do the indexing of the numbers starting from the right. For example we have 231₅, so starting from 1 to have index 0, 3 to have index 1 and 2 to have index 2, now to convert it to decimal format, multiply the digits with 5 to the power of its index.

231₅=2*10²+3*10¹+1*10⁰=66 now to convert 66₁₀ to the format of base 16, divide it by 16 and write the remainder seperately, s we get 42₁₆.

A. Now in a octal(base 8) system the numbers allowed are from 0 to 7 , in decimal(base 10) system the numbers allowed are 0 to 9.

So in a system having base 7, the numbers allowed are from 0 to 6, we cannot allow any other number other than this, so in Part A as the Figure given is 66067₇ is not valid.

B. 240311₅=2*5⁵+4*5⁴+0*5³+3*5²+1*5¹+1*5⁰=8831₁₀

Now dividing 8831 by 16 and writing the remainders to convert it to base 16 we get 227F, where in hexadecimal A=10,B=11,C=12,D=13,E=14,F=15 as hexa decimal has base 16 so the numbers allowed are from 0 to 15.

C. 2361511₉=2*9⁶+3*9⁵+6*9⁴+1*9³+5*9²+1*9¹+1*9⁰=1280539₁₀

Now dividing 1280539 by 16 and writing the remainders to convert it to base 16 we get 138A1B, where in hexadecimal A=10,B=11,C=12,D=13,E=14,F=15 as hexa decimal has base 16 so the numbers allowed are from 0 to 15.

D. (1101101101110111011011100110101011)₂=(155567334653)₈

There is a Shortcut method to convert binary to octal, you dont need to convert binary to decmal and then decimal to octal you just need to make groups of 3 starting from the most right corner and whrite its corrosponding value.As we know 101 is 5, similiarly 111 is 7, 010 is 2 and so on, so on dividing the binary number in groups of 3 we get

1 101 101 101 110 111 011 011 100 110 101 011

Add zeroes to the last digit to make it a group of 3

001 101 101 101 110 111 011 011 100 110 101 011

1 5 5 5 6 7 3 3 4 6 5 3

So this is the Octal conversion of Binary.

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