Name: Abdullah Abdulrahman Muhammed Omar
Reg No.: 227584
Assignment 1
1) Find the logic function
2) Then simplify the function
3) Find the logic circuit
The variables are a,b,c,d
Note:
F= m0,m4,m8,m10.m14.m15
The Truth Table:
A
B
C
D
F
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
Logic Function:
̅ 𝑩 ̅̅̅̅̅
̅̅̅̅̅̅̅̅
̅ 𝑪𝑫
̅ + 𝑨𝑩𝑪𝑫
̅ + 𝑨𝑩𝑪𝑫
F= ̅̅̅̅̅̅̅̅̅̅
𝑨 𝑩 𝑪 𝑫+ 𝑨
𝑪𝑫+ 𝑨𝑩
𝑪𝑫+ 𝑨𝑩
̅ 𝑪̅ 𝑩
̅ + 𝑪) + 𝑨 𝑩 𝑪(𝑫
̅ (𝑩
̅ + 𝑩) + 𝑨 𝑩
̅𝑫
̅ (𝑪
̅ + 𝑫)
F= 𝑨
̅ 𝑪̅ 𝑩
̅ + 𝑨𝑩
̅𝑫
̅ + 𝑨𝑩𝑪
F= 𝑨
Logic Circuit:
̅ 𝑪̅ 𝑩
̅ + 𝑨𝑩
̅𝑫
̅ + 𝑨𝑩𝑪
According to : F= 𝑨
Assignment (2)
o Design a circuit with three inputs and one output, F=0, If the sum of inputs
greater or equal to 2 .
Truth Table:
X
Y
Z
F
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
K-Map:
𝑌̅𝑍̅
1
𝑋̅
X 0
F=Σm0,m1
̅𝒀
̅𝒁
̅+𝑿
̅𝒀
̅𝒁
Logic Function = 𝑿
̅𝒀
̅ (𝒁
̅ + 𝒁)
Simplify the function: 𝑭 = 𝑿
̅𝒀
̅ (1)
𝑭=𝑿
̅𝒀
̅
𝑭=𝑿
Applying Logic circuit:
𝑌̅Z
1
Y𝑍̅
0
0
0
0
0
YZ