Binary, Decimal: A 12 bit (binary digit) number, consisting of 8 integer bits and...

[xoxo9931]

Is anyone kind enough to show and teach me how to do this qn?

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) How many different numbers can be sent via this channel?
b) What is the maximum number (in decimal) that can be sent?
c) List all the numbers (in decimal) that can be sent via this channel, between 1.25 and 1.5 inclusive.
d) Alex wants to send a decimal value of 37.625 to Better via this communication channel. How will the transmitted channel look like?




Ans:
a) 4096
b)255.9375
c)1.25, 1.3125, 1.375, 1.4375. 1.5
d) 0010 0101 .1010

 

[ksdhart2]

Is anyone kind enough to show and teach me how to do this qn?

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) How many different numbers can be sent via this channel?
b) What is the maximum number (in decimal) that can be sent?
c) List all the numbers (in decimal) that can be sent via this channel, between 1.25 and 1.5 inclusive.
d) Alex wants to send a decimal value of 37.625 to Better via this communication channel. How will the transmitted channel look like?


Ans:
a) 4096
b)255.9375
c)1.25, 1.3125, 1.375, 1.4375. 1.5
d) 0010 0101 .1010

Well, I'd venture that you were given this question for a reason, so what I wonder now is: What has your class recently been learning about binary? You may also find it useful to review the concepts involved in binary at this website and this other website.

a) You have 12 digits, eight preceding the decimal point and four following it. Each of these digits can be either a 0 or a 1. Every unique combination of 1s and 0s represents a number, so how many combinations are there? As a hint, you may want to consider what would happen if you were working with just one digit, then two digits, then three, etc. See if you can find a pattern that helps you solve the larger case.

b) Here you'll need to know how to compare two binary numbers. Which of these two is bigger: 100101 or 1000100. Why? Which of these two is bigger: 0001 or 1111? Why? What does that suggest about what the largest binary number with a given number of digits would look like? How would you convert that largest binary number with 12 digits to standard decimal representation?

c) What does the decimal number 1.25 look like in binary? What does the decimal number 1.5 look like in binary? How many binary numbers fall between these two numbers? As a hint, consider that 1.25 = 1 + 1/4 = 2⁰ + 1/2²

d) What does the decimal number 37.625 look like in binary?

Hopefully these should be enough to at least get you started. If you get stuck again, that's okay, but when you reply back, please comply with the rules as laid out in the Read Before Posting thread that's stickied at the top of every sub-forum, and include all of your work and thoughts on these problems, even including the parts you know for sure are wrong. Thank you.