Floating point numbers are quite interesting in how they are stored, as detailed in this article for 32 bit floating point numbers using the ieee-754 standard. it is conceptually based on base 2 scientific notation: (mantissa) x 2 so there are three parts we need: the sign, the exponent n, and the mantissa, and we need to pack them all into a 32 bit code. engineers being engineers, how this coding is done is 'creative as detailed the linked article the format is: a sign bit; 8 bits for exponent coded as an 8 bit unsigned integer minus 127; followed by 23 bits for the 24 bit mantissa (written in decimal form). in binary decimal, the first digit of the mantissa is always 1, so does not actually have to be written down. so as detailed above, a 32 bit number is written in three segments: sign in 1 bit; 8 bits to code a positive integer (-127) for the exponent; and 23 bits for the 24 bit mantissa. the mantissa is in decimal format, so if list the 24 bits as mo. m (where m. .m23 is written down and mo-1 is implicit). this is equal to mox 2+mx 21+m2x 22+. m23 x 223 1) show that 01 000 0 0 0 01 0 0 1 0 0 1 0 0 0 01 1 0 1 1011 is a fairly accurate representation of pi, explaining how you unpacked the number. [note that multiplying by the 2" part can make a number appear very different in base10 2) pick your favorite physical constant (e. g. speed of light, radius of the earth, mass of the electron, etc.) and code it as a 32 bit float. explain how you did it. 3) in the last homework you built a circuit that would add integers. describe, using words and drawings, how you would build a circuit to add floating point numbers.