To subtract the binary numbers [tex]\(1001_2\)[/tex] and [tex]\(110_2\)[/tex], follow these steps:
1. Convert the binary numbers to decimal form:
- The binary number [tex]\(1001_2\)[/tex] can be converted to a decimal:
[tex]\[ 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 = 8 + 0 + 0 + 1 = 9 \][/tex]
So, [tex]\(1001_2\)[/tex] is [tex]\(9_{10}\)[/tex] in decimal form.
- The binary number [tex]\(110_2\)[/tex] can be converted to a decimal:
[tex]\[ 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 = 4 + 2 + 0 = 6 \][/tex]
So, [tex]\(110_2\)[/tex] is [tex]\(6_{10}\)[/tex] in decimal form.
2. Subtract the decimal numbers:
[tex]\[ 9 - 6 = 3 \][/tex]
3. Convert the result back to binary form:
- The decimal number [tex]\(3\)[/tex] can be converted to binary by finding which powers of 2 sum up to [tex]\(3\)[/tex]:
[tex]\[ 3 = 2^1 + 2^0 \][/tex]
So, [tex]\(3_{10}\)[/tex] is represented as [tex]\(11_2\)[/tex] in binary form.
4. Compile the results:
- The decimal equivalents of the binary numbers are [tex]\(9_{10}\)[/tex] and [tex]\(6_{10}\)[/tex].
- The subtraction of these decimal numbers gives [tex]\(3_{10}\)[/tex].
- The binary representation of the result is [tex]\(11_2\)[/tex].
Hence, the subtraction [tex]\(1001_2 - 110_2\)[/tex] results in [tex]\(11_2\)[/tex].
