To determine which ASCII character is represented by the binary number [tex]\( 1001010 \)[/tex], follow these steps:
1. Understand the binary number system: A binary number is composed of two symbols, 0 and 1, and each position in a binary number represents a power of 2, starting from [tex]\( 2^0 \)[/tex] on the far right.
Let's first write down the binary number [tex]\( 1001010 \)[/tex]:
[tex]\[
1001010
\][/tex]
2. Convert the binary number to decimal: To convert binary [tex]\( 1001010 \)[/tex] to its decimal equivalent, calculate the value for each bit that is set to 1. The binary number [tex]\( 1001010 \)[/tex] represents:
[tex]\[
1 \cdot 2^6 + 0 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0
\][/tex]
Let's compute these values separately and then sum them:
[tex]\[
1 \cdot 64 + 0 \cdot 32 + 0 \cdot 16 + 1 \cdot 8 + 0 \cdot 4 + 1 \cdot 2 + 0 \cdot 1
\][/tex]
Breaking it down:
[tex]\[
64 + 0 + 0 + 8 + 0 + 2 + 0 = 74
\][/tex]
Therefore, the decimal equivalent of the binary number [tex]\( 1001010 \)[/tex] is [tex]\( 74 \)[/tex].
3. Determine the corresponding ASCII character: Consult the provided ASCII table to find the character that corresponds to the decimal value [tex]\( 74 \)[/tex].
According to the table:
[tex]\[
74 \quad \rightarrow \quad J
\][/tex]
Therefore, the binary number [tex]\( 1001010 \)[/tex] represents the ASCII character [tex]\( J \)[/tex].
