Perform the binary floating-point addition of the following two numbers given in

Question

Perform the binary floating-point addition of the following two numbers given in 32-bit IEEE floating-point format. You must unpack them, align the mantissas, perform the addition in binary, normalize, and express the result in 32-bit IEEE floating-point format. $414A000016                $4030000016 Perform the binary floating-point addition of the following two numbers given in 32-bit IEEE floating-point format. You must unpack them, align the mantissas, perform the addition in binary, normalize, and express the result in 32-bit IEEE floating-point format. $414A000016                $4030000016

Explanation / Answer

414A0000,the unpacked binary format=01000001010010100000000000000000

Bit 31,Sign=0, so its positive value

Bits 30 - 23 Exponent Field =10000010;decimal value is 130-127=3

Bits 22 - 0 Significand=1 .10010100000000000000000,the decimal value is 1.5781250

The deimal representation is 12.625000

The binary representation of 12.625000=1100.10100000

40300000,the unpacked binary format=01000001010010100000000000000000

Bit 31,Sign=0, so its positive value

Bits 30 - 23 Exponent Field =10000000;decimal value is 128-127=1

Bits 22 - 0 Significand=1 .01100000000000000000000,the decimal value is 1.3750000

The deimal representation is 2.7500000;

The binary representation of  2.7500000=10.11000000

The binary addition 1100.10100000+10.11000000=1111.01100000

The decimal value of Addition=15.375

32-bit IEEE floating-point format in binary=01000001011101100000000000000000,

32-bit IEEE floating-point hexa decimal value=$(41760000)16

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