Final answer:
To represent the decimal number 13.5 in IEEE 754 single-precision floating-point format, convert it into binary and determine the sign bit, exponent, and mantissa.
Step-by-step explanation:
To represent the decimal number 13.5 in IEEE 754 single-precision floating-point format, we first need to convert it into binary representation. The integer part of the number, 13, can be represented in binary as 1101. The fractional part, 0.5, can be converted into binary by multiplying it by 2 repeatedly until we reach the desired precision. So, 0.5 x 2 = 1.0, the integer part becomes 1 and the fractional part becomes 0.0. Therefore, the binary representation of 13.5 is 1101.1.
Next, we need to determine the sign bit. Since the number is positive, the sign bit is 0.
Now, we need to calculate the exponent. The binary representation of 13.5 has a decimal point after the first bit, so we need to shift the decimal point to the right by 3 places to normalize the number. This gives us 1.101 x 2^3.
The exponent is calculated as (3 + 127) = 130. In binary, 130 is 10000010. Therefore, the exponent is 10000010.
The final step is to represent the fractional part in 23 bits. In this case, since we only have one fractional bit, we fill the remaining 22 bits with zeros. So the mantissa becomes 10100000000000000000000.
Putting it all together, the IEEE 754 single-precision floating-point representation of 13.5 is:
0 10000010 10100000000000000000000