Booth's coding is a way to represent signed integers in binary format. It was invented by Andrew Donald Booth in 1950. It uses a combination of two's complement and signed-digit representation to reduce the number of operations required for multiplication.
To convert a decimal number to Booth's coding in 8 bits, we follow these steps:
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Convert the decimal number to its two's complement representation in 8 bits. To do this, we first convert the absolute value of the decimal number to binary, and then take the two's complement of the binary number. In this case, the absolute value of -57 is 57, which in binary is 00111001. Taking the two's complement of this gives us 110010111.
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Add a zero at the beginning of the binary number to indicate that it is positive. This gives us 0110010111.
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Group the binary number into pairs of two, starting from the right. This gives us 01 10 01 01 11.
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For each pair of bits, replace 01 with 0-1 and 10 with 1-0. This gives us 0-1 1-0 0-1 0-1 1-1.
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Concatenate the resulting 5 pairs of bits to get the final Booth's coding in 8 bits. This gives us 0-101001011.
Therefore, the correct option is B) 0-100+100-1, which represents the Booth's coding of -57 in 8 bits.
