Each section of the binary number represents a different component needed to construct the number 300. It uses clever math to be able to represent decimals. It’s like asking you whether a number is positive or negative, then the position of the decimal point, then what the digits are.
Specifically…
The first 0 means the number is positive. The number formed by the next eight bits (the exponent) and the number from the remaining bits (the mantissa) multiply to get 300.
The exponent bits choose the value of N in the formula 2N-127 . For the mantissa, we start with the number 1, then each “1” bit starting from the left adds to it 0.5, then 0.25, and so on. Specifically, we have 28×1.171875.
For those who are curious, that’s the IEEE 754 representation of the number 300.
That was a very good guess!
What? Why?
Each section of the binary number represents a different component needed to construct the number 300. It uses clever math to be able to represent decimals. It’s like asking you whether a number is positive or negative, then the position of the decimal point, then what the digits are.
Specifically…
The first 0 means the number is positive. The number formed by the next eight bits (the exponent) and the number from the remaining bits (the mantissa) multiply to get 300.
The exponent bits choose the value of N in the formula 2N-127 . For the mantissa, we start with the number 1, then each “1” bit starting from the left adds to it 0.5, then 0.25, and so on. Specifically, we have 28×1.171875.
Aaaaaaaaaghhhh bitwise arithmetic aaaaaahhhhffggffg it’s all coming back YOU DON’T KNOW WHAT YOU’VE UNLEASHED KHGHHAAAA
But thank you for the explanation