Answer:
Explanation:
To work out the given expression without a calculator, we need to convert the numbers from their respective bases to decimal form and then perform the arithmetic operations. Let's break it down step by step:
11101010 base 2: To convert a binary number to decimal, we multiply each digit by the corresponding power of 2 and sum the results. So, let's calculate:
1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 234.
2122 base 8: To convert an octal number to decimal, we multiply each digit by the corresponding power of 8 and sum the results. Let's calculate:
2 * 8^3 + 1 * 8^2 + 2 * 8^1 + 2 * 8^0 = 1090.
ABC base 16: To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum the results. Let's calculate:
10 * 16^2 + 11 * 16^1 + 12 * 16^0 = 2748.
123 base 8: We already know that 123 is in base 8 (octal), so we can directly convert it to decimal:
1 * 8^2 + 2 * 8^1 + 3 * 8^0 = 83.
Now, let's perform the arithmetic operations:
234 + 1090 + 2748 - 83 = 3989.
Therefore, the result of the given expression in decimal form is 3989.