To convert the hexadecimal value "CAB" into another numeral system, let's break it down step-by-step. Remember that hexadecimal (base-16) digits range from 0 to F, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.
### Conversion to Binary
1. Break down each hexadecimal digit to its binary equivalent:
- [tex]\( C \)[/tex] in hexadecimal is 12 in decimal, and [tex]\( 12 \)[/tex] in binary is [tex]\( 1100 \)[/tex].
- [tex]\( A \)[/tex] in hexadecimal is 10 in decimal, and [tex]\( 10 \)[/tex] in binary is [tex]\( 1010 \)[/tex].
- [tex]\( B \)[/tex] in hexadecimal is 11 in decimal, and [tex]\( 11 \)[/tex] in binary is [tex]\( 1011 \)[/tex].
2. Combine the binary equivalents:
[tex]\[
\text{Hex} \ "C" = \text{Binary} \ "1100" \\
\text{Hex} \ "A" = \text{Binary} \ "1010" \\
\text{Hex} \ "B" = \text{Binary} \ "1011"
\][/tex]
Now concatenate these binary values:
[tex]\[
\text{Hex} \ "CAB" = \text{Binary} \ "1100 1010 1011"
\][/tex]
3. Remove spaces:
[tex]\[
\text{Binary} \ "110010101011"
\][/tex]
Therefore, the correct binary conversion of "CAB" is:
[tex]\[ \text{Binary string} \ "110010101011" \][/tex]
Among the provided choices, the binary string that accurately represents the hexadecimal "CAB" is:
[tex]\[ \boxed{\text{110010101011}} \][/tex]
