To subtract the binary numbers \( 1001010_2 \) and \( 10101_2 \), let's first convert them to decimal, perform the subtraction, and then convert the result back to binary.
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Convert \( 1001010_2 \) to decimal:
- \( 1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 \)
- \( = 64 + 0 + 0 + 8 + 0 + 2 + 0 = 74_{10} \)
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Convert \( 10101_2 \) to decimal:
- \( 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 \)
- \( = 16 + 0 + 4 + 0 + 1 = 21_{10} \)
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Perform decimal subtraction:
- \( 74 - 21 = 53 \)
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Convert \( 53_{10} \) back to binary:
- Divide 53 by 2, record the remainder:
- \( 53 \div 2 = 26 \) remainder \( 1 \)
- \( 26 \div 2 = 13 \) remainder \( 0 \)
- \( 13 \div 2 = 6 \) remainder \( 1 \)
- \( 6 \div 2 = 3 \) remainder \( 0 \)
- \( 3 \div 2 = 1 \) remainder \( 1 \)
- \( 1 \div 2 = 0 \) remainder \( 1 \)
- Reading the remainders from bottom to top: \( 110101_2 \)
- Divide 53 by 2, record the remainder:
Thus, the result of \( 1001010_2 - 10101_2 \) is \( 110101_2 \).