Question 1: (10+ 10- 20 points) (a) Fill in each blank. [10 points, -1 per wrong
ID: 3918716 • Letter: Q
Question
Question 1: (10+ 10- 20 points) (a) Fill in each blank. [10 points, -1 per wrong or blank answer, min O] 1) The 6-bit signed-2's representation of a decimal number (-10) is 2) The canonical sum-of-product representation of (AB' +AC) is 3) A 4 to 1 MUX has 5) The characteristic equation of a JK flip-flop is selection lines and output line(s). 4) A decoder with N inpus has a maximum of outputs. 6) To cause the required transition of Qu-t) Qo for a T flip-flop, the required input 1s (b) Convert A (10.5)o and B- (8.25)10 into binary format using 6 bits for the integer part and 3 bits for the fractional part, including the sign bit. Perform the following operations in specific signed complement as indicated for each operation. using signed I's complement using signed 2's complement (ii) D-A+ B Important note: Explain clearly your solution! Please note that if you give directly the result of the conversion of the two numbers (A and B), without explaining the conversion method you have used, your mark for this part of the question will be zero!Explanation / Answer
A)
1)
10 => 0 01010
01010 => 2’s complement
-10 => 1 10110
2)
Canonical sum of product:
AB’+ AC’
=>AB’(C+C’) +AC’(B+B’)
=>AB’C + AB’ C’ + AC’B + AC’B’
3)
Select lines = LOG(4) base 2= 2
Output lines = 1
Input lines = 4
4)
Decoder with n inputs have maximum 2^n outputs.
5)
Characteristic equation of JK flipflop:
Qnext = JQ’ + K’Q
6)
The required transition here is previous state of T flipflop is same as current state.
Means no change in state. It’s called latch state.
Required input for T is 0.
b)
i)
(10.5) = 001010.100
(8.25) = 001000.010
C=A – B
-B in one’s complement => 110111.101
A+(-B) =
001010.100
110111.101
------------------
Carry should be wrap around in 1’s complement addition
000010.001
+ 1
--------------
000010.010
=>2.25
ii)
2’s complement
(10.5) = 001010.100
(8.25) = 001000.010
-A:
110101. 011
+ 1
----------------
110101.100
------------
D= B-A
=B+(-A)
001000.010
110101.100
--------------------
111101.110
--------------
As there is no carry, result is –ve number.
Let’s DO 2’s complement for result
000010.001
+ 1
------------------
000010.010
-----------------
Number is :- - (2.25)
Comment below if you have any doubt
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.