Truth table

[magneticloud]

දන්න කෙනෙක් මේක ටික කියලා දෙන්න


A digital circuit has four inputs D, C, B, A representing the binary values 0000 to 1111 (i.e., 0 to 15 decimal). The output F is true if the input fails in the range 8 to 10 (inclusive),or if the input is divisible by 3, or if the input is divisible by 7.it if false otherwise. zero is considered as indivisible by 3 or 7


a)construct a truth table for system
b)from the truth table write down a boolean equation for F in terms of D,C,B,A
c)using either boolean algebra or Karnaugh maps,obtain a simplified expression for F
d)draw a circuit to implement the circuit for F

 

[imhotep]

Just a hint.... First do the Truth Table. F as output , inputs D C B A
F will be only True for decimal 8,9 & 10 which is
1 0 0 0 D barC bar B bar A
1 0 0 1 D barC barB A
1 0 1 0 D barC B barA

Do the above for decimal 3, 6, 12, 15, 7 & 14 (since its's true for these numbers as well)

Then add up all these to get the sum of products expression. Simplify it as much as you can using the theorems and then you can get the circuit implementation.

 

[saja]

same type question

BCS THE CHARTERED INSTITUTE FOR IT
BCS HIGHER EDUCATION QUALIFICATIONS
BCS Level 4 Certificate in IT
COMPUTER & NETWORK TECHNOLOGY
Thursday 26th March 2015 - Morning

A4 A combinational logic circuit has four inputs D, C, B, A representing the binary values 0000 to 1111 (i.e., 0 to 15 decimal). The output F is 1 if the decimal input on DCBA is divisible by 4 or by 7.
a) Draw a truth table for this system
(8 marks)
b) Obtain an expression for F from the truth table
(7 marks)
c) Obtain a simplified expression for F using either Boolean algebra or a Karnaugh map. (8 marks)
d) Suppose that the input DCBA = 1111 could never occur and does not need to be considered. Obtain a new simplified expression for F taking this don’t care condition into account.

answer

https://www.bcs.org/get-qualified/i...exam-reports/computer-and-network-technology/

දන්න කෙනෙක් මේක ටික කියලා දෙන්න


A digital circuit has four inputs D, C, B, A representing the binary values 0000 to 1111 (i.e., 0 to 15 decimal). The output F is true if the input fails in the range 8 to 10 (inclusive),or if the input is divisible by 3, or if the input is divisible by 7.it if false otherwise. zero is considered as indivisible by 3 or 7


a)construct a truth table for system
b)from the truth table write down a boolean equation for F in terms of D,C,B,A
c)using either boolean algebra or Karnaugh maps,obtain a simplified expression for F
d)draw a circuit to implement the circuit for F

 

[hodakolla]

BUMPER

 

[magneticloud]

BUMP

 

[imhotep]

D C B A Output F
______________________________
0 0 0 0 False 0
0 0 0 1 False 0
0 0 1 0 False 0
0 0 1 1 True 1
0 1 0 0 False 0
0 1 0 1 False 0
0 1 1 0 True 1
0 1 1 1 True 1
1 0 0 0 True 1
1 0 0 1 True 1
1 0 1 0 True 1
1 0 1 1 False 0
1 1 0 0 True 1
1 1 0 1 False 0
1 1 1 0 True 1
1 1 1 1 False 0

From the truth table the SOP is

F = D! C! B A + D! C B A! + D! C B A + D C! B! A! + D C! B! A + D C! B A! + D C B! A! + D C B A!

Use the theorems in Boolean algebra to simply it.....

 

[salitha22]

melo deyak terune na ban