Consider the following IEEE 754 32-bit floating point value:01001111 01001000 00000000 00000000Enter S, its sign, as either + or -. Enter E, its exponent part's value, in base 10.
Question
Consider the following IEEE 754 32-bit floating point value:01001111 01001000 00000000 00000000Enter S, its sign, as either + or -. Enter E, its exponent part's value, in base 10.
Solution
The IEEE 754 32-bit floating point value is divided into three parts: the sign bit, the exponent, and the mantissa.
-
Sign bit (S): The first bit is the sign bit. If the sign bit is 0, then the number is positive. If it's 1, the number is negative. In this case, the sign bit is 0, so S is +.
-
Exponent (E): The next 8 bits are the exponent, expressed as a binary number. In this case, the exponent is 01001111, which is 79 in decimal. However, the IEEE 754 standard represents the exponent with a bias of 127, so we subtract 127 from the exponent to get the actual value. So, E is 79 - 127 = -48.
So, the sign S is + and the exponent E is -48.
Similar Questions
Single-precision IEEE-754 floating-point numbers are represented as follows:(-1)S * (1.M)*2(E - Bias)(Bias = 127)For the binary value 11000010 01111001 00000000 00000000 in single-precision IEEE-754floating point form, convert it to its decimal representation.S = 1 so negative numberExponent = 10000100 = 128 + 4 = 132132 – 127 (bias) = 5Mantissa = 1.1111001Shift binary point 5 spaces = 111110.01Translate LHS = 2+4+8+16+32 (or 64-2) = 62Translate RHS = 0.25S+LHS+RHS = -62.25(6 marks)S Expon
Construct -33.75 to IEEE 754 Single precision floating point number. Explainhow zero is represented in this format.
In the IEEE 754 standard, what components make up the floating-point representation of a number?
Represent the following as a single precision floating point (IEEE 754) number:a) 85.125b) -4.75
4. Represent the following as a single precision floating point (IEEE 754) number:a) 85.125b) -4.75
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.