Math

QuestionConvert the hexadecimal number 1F1\mathrm{F} (base 16) to its binary equivalent.

Studdy Solution

STEP 1

Assumptions1. We are converting from hexadecimal (base16) to binary (base). . The hexadecimal number is1.

STEP 2

First, we need to understand the relationship between hexadecimal and binary. Each hexadecimal digit can be represented by four binary digits, as follows0000010001200100011401005010160110701118100091001A1010B1011C1100110111101111\begin{align*} 0 &0000 \\ 1 &0001 \\ 2 &0010 \\ &0011 \\ 4 &0100 \\ 5 &0101 \\ 6 &0110 \\ 7 &0111 \\ 8 &1000 \\ 9 &1001 \\ A &1010 \\ B &1011 \\ C &1100 \\ &1101 \\ &1110 \\ &1111 \\ \end{align*}

STEP 3

Now, we can convert each digit of the hexadecimal number into binary. Start with the first digit,1. Looking at the table above, we see that1 corresponds to0001 in binary.
116=000121_{16} =0001_{2}

STEP 4

Next, convert the second digit, F. According to the table, F corresponds to1111 in binary.
16=11112_{16} =1111_{2}

STEP 5

Combine the binary equivalents of the two digits to get the binary representation of the hexadecimal number.
116=0001111121_{16} =0001\,1111_{2}

STEP 6

Finally, remove any leading zeros. In this case, we can remove the three leading zeros from the binary number.
000111112=1111120001\,1111_{2} =1\,1111_{2}The hexadecimal number1 is equal to the binary number11111.

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