Question Detail

To convert a long binary number to hexadecimal, the easiest way is to group the digits into sets of four, starting from the right. Each group of four binary digits corresponds to exactly one hexadecimal digit. Step 1: Group by 4 (from right to left) The binary number is $10010111101100100111_{2}$. We break it into groups of four: 1001 | 0111 | 1011 | 0010 | 0111 Step 2: Convert each group to Hex Using the standard conversion (8-4-2-1 rule):

• 1001: $8 + 0 + 0 + 1 = 9$ $\rightarrow$ 9
• 0111: $0 + 4 + 2 + 1 = 7$ $\rightarrow$ 7
• 1011: $8 + 0 + 2 + 1 = 11$ $\rightarrow$ B (In hex, 10=A, 11=B, 12=C...)
• 0010: $0 + 0 + 2 + 0 = 2$ $\rightarrow$ 2
• 0111: $0 + 4 + 2 + 1 = 7$ $\rightarrow$ 7

Step 3: Combine the results Putting them all together: 9 7 B 2 7 The hexadecimal equivalent of $10010111101100100111_{2}$ is $97B27_{16}$.