convert 1.75 to floating point representation IEEE 1958

Sure, I can help you with that.

To convert 1.75 to floating point representation IEEE 1958, we need to follow certain steps:

Step 1: Convert the decimal number 1.75 to binary.
1. Convert the integer part 1 to binary -> 1
2. Convert the fraction part 0.75 to binary:
0.75 x 2 = 1.5 (1 goes to the bit after the comma)
0.5 x 2 = 1 (1 goes to the next bit)
0

So 1.75 in binary is represented as 1.11

Step 2: Normalize the binary number
The binary number is normalized by moving the decimal point to the left so that there is only one non-zero digit before the decimal point. In this case, the binary number is already normalized.

Step 3: Determine the sign, exponent, and mantissa
Sign: Since the number is positive, the sign bit is 0.
Exponent: The exponent can be calculated using the formula:

exponent = (number of bits for exponent - 1) + bias

For IEEE 1958 floating point representation, the bias value is 127, and the number of bits for the exponent is 8.
In this case, the exponent is 0 + 127 = 127

Mantissa: The mantissa is the fractional part of the normalized binary number.
In this case, the mantissa is 1.11, which can be represented as:

1.11 = 1 + 1/2 + 1/4 = 1.5

The mantissa is then represented in binary as:

1.5 = 1.1000...

So the sign bit is 0, the exponent in binary is 01111111, and the mantissa in binary is 10000000000000000000000.

Putting it all together, 1.75 in floating point representation IEEE 1958 is:

0 11111111 10000000000000000000000

I hope this helps! Is there anything else I can assist you with?