# How to find the bits that fall between two given bits?

A 12-bit(binary-digit) number, consisting of 8 integer bits and 4 fractional bits, is to be sent from a sender to a receiver via a wireless communication channel.

a) List all the numbers(in decimal) that can via this channel, between 1.25 and 1.5 inclusive.

I know that for this question, they are asking me to find the numbers that fall between 1.25 and 1.5. Hence, I change those two numbers into bits. 1.25 = 1.01 1.5 = 1.0

Hence 1.01-----------------------1.0 The problem I am facing now is i do not know how to get the bits withnin the range of 1.01 to 1.0.

Ans: 1.25,1.3125,1.375,1.4375,1.5

$1.25_{10}=1.0100_2, 1.5_{10}=1.1000_2$, where you should list the numbers out to four bits past the radix point as specified. Now you need to list all the numbers in between and convert them to base $10$. An easier approach is to note that the interval between numbers is $0.0001_2=0.0625_{10}$ and just add that much to $1.25_{10}$ until you get to $1.5_{10}$