Question

question 19
the hexadecimal equivalent for 1100 1010 0111 1001₂ is:
da87.
ca87.
da79.
ca79.

Explanation:

Step1: Group the binary digits

Group the binary number \(1100\ 1010\ 0111\ 1001_2\) into groups of 4 bits from right to left: \(1100\), \(1010\), \(0111\), \(1001\).

Step2: Convert each group to hexadecimal

• For \(1100_2\): \(1\times2^3 + 1\times2^2+0\times2^1 + 0\times2^0=8 + 4+0 + 0 = 12\). In hexadecimal, \(12\) is \(C\).
• For \(1010_2\): \(1\times2^3+0\times2^2 + 1\times2^1+0\times2^0=8+0 + 2+0 = 10\). In hexadecimal, \(10\) is \(A\).
• For \(0111_2\): \(0\times2^3+1\times2^2 + 1\times2^1+1\times2^0=0 + 4+2 + 1=7\). In hexadecimal, \(7\) is \(7\).
• For \(1001_2\): \(1\times2^3+0\times2^2+0\times2^1 + 1\times2^0=8+0+0 + 1 = 9\). In hexadecimal, \(9\) is \(9\).

Combining these results, we get \(CA79\).

Answer:

C. DA79