Let's solve the given question step by step:
We are given a function [tex]\( f(x) = (10 - x)_2 \)[/tex]. This notation indicates that [tex]\( 10 - x \)[/tex] is to be evaluated in base 2 (binary).
Step 1: Calculate [tex]\( f(6) \)[/tex]
First, substitute [tex]\( x = 6 \)[/tex] into the function:
[tex]\[ f(6) = (10 - 6)_2 \][/tex]
Subtract to get:
[tex]\[ 10 - 6 = 4 \][/tex]
So, we need to represent 4 in base 2 (binary). In binary, [tex]\( 4 \)[/tex] is written as [tex]\( 100_2 \)[/tex].
Hence, [tex]\( f(6) \)[/tex] evaluated in binary is 4 (but we keep it as a decimal here for simplicity).
So,
[tex]\[ p = f(6) = 4 \][/tex]
Step 2: Calculate [tex]\( 4p \)[/tex]
Now we need to find [tex]\( 4p \)[/tex]:
[tex]\[ 4p = 4 \times 4 \][/tex]
Multiply these values:
[tex]\[ 4 \times 4 = 16 \][/tex]
Finally, [tex]\( 4p \)[/tex] is:
[tex]\[ \boxed{16} \][/tex]
Therefore, [tex]\( 4p \)[/tex] is 16.
