Convert Binary Numbers to Decimal Numbers

What is the decimal equivalent of the binary number 1100 1001?

The decimal equivalent of the binary number 1100 1001 is -28. In binary to decimal conversion, each bit of the binary number represents a power of 2. Starting from the rightmost bit, the values of the bits are calculated by multiplying the bit with 2 raised to the power of its position from right to left. In this case, the decimal conversion follows as: 1 * 2^7 + 1 * 2^6 + 0 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0 = 128 + 64 + 0 + 0 + 8 + 0 + 0 + 1 = 201 However, since the leftmost bit is 1, the number is considered as negative in Two's complement representation. Therefore, the decimal equivalent of the binary number 11001001 is -28.

Binary to Decimal Conversion:

Binary to Decimal conversion is a process of converting a binary number to its equivalent decimal form. In binary numbers, each digit represents a power of 2, starting from 2^0 on the rightmost digit. By multiplying each bit with 2 raised to the power of its position and summing up the results, we can obtain the decimal equivalent of the binary number.

Two's Complement Representation:

Two's Complement representation is used to represent negative numbers in binary form. In this representation, the leftmost bit of a binary number indicates its sign. If the leftmost bit is 0, the number is positive; if the leftmost bit is 1, the number is negative. To find the value of a negative binary number in Two's Complement representation, first invert all bits and then add 1 to the result.