Perform the following conversions to the indicated bases

Perform the following conversions to the indicated bases:

(973)10 = (?)5

(F23A)16 = (?)8

(10110.11)2 = (?)10

Let's perform the given conversions step by step.

We repeatedly divide 973 by 5 and record the remainders.

973÷5=194 remainder 3

194 ÷ 5 = 38 remainder 4

38 ÷ 5 = 7 remainder 3

7 ÷ 5 = 1 remainder 2

1 ÷ 5 = 0 remainder 1

Reading the remainders from bottom to top, (973)₁₀ = (12343)₅.

First, convert from hexadecimal (base 16) to binary.

F=1111, 2=0010, 3=0011, A=1010

So, (F23A)₁₆ in binary:

F23A=1111 0010 0011 1010

Now, group into triplets from right to left for conversion to octal:

1 111 001 000 111 010

Converting each triplet to octal:

1=1,111=7,001=1,000=0,111=7,010=2

So, (F23A)₁₆ = (171072)₈.

We expand the binary number using powers of 2.

Thus, (10110.11)₂ = (22.75)₁₀.

Final Answers:

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