We are given a digital thermometer that digitizes a temperat

We are given a digital thermometer that digitizes a temperature into an 8-bit unsigned binary num- ber C representing the temperature in Celsius. For example, 30 degrees Celsius would be digitized as 00011110. We want to convert that temperature to Fahrenheit, again using 8 unsigned bits. The equation for converting is: F = C*9/5 + 32 We can rewrite the equation as: F = C + C*4/5 + 32 C*4/5 is 4*(C/5). We saw above that C/5 can be closely approximated as: (C*64+C*32+C*4+C*2)/512 The multiplication of the above equation by 4 to obtain 4*(C/5) changes the denominator to 128. Thus, the equation for converting can be rewritten as: F = C+(C*64+C*32+C*4+C*2)/128+32

My question is how the function can be re-writen as C + C*4/5 + 32?

Solution

F = C* 9/5 + 32 can be written as

F = C* (5+4)/5 + 32

F = C* 5/5 + C* 4/5 + 32

F= C + C* 4/5 + 32

Therefore the function can bre re-written as C + C*4/5 + 32.