Simplify the following Boolean function f using K-map: m x1 x2 x3 x4 f 0 0000 1 1 0 0 0 1 1 234 10 0 0 1 0 1 0 0 1 1 X 0 1 0 0 0 5 01 0 1 0 6 0 1 1 0 1 7 0 1 1 1 0 8 1 9 1 10 1 11 12 13 0 0 0 X 001 0 1 0 1 10 110 1100 1101 0 14 1110 0 X X 15 1 1 1 10 f=Σ m(0,1,2,6,10) & don't care X=Σ m(3,8,13,14) 3- Write the function in terms of x1, x2, x3 and x4 after K-map: Σ(0, 1, 2, 6, 10) f = X • X₁₂ • X + ×₁ • x₂ 3 X ׸ • × + ×₁ • X₂ •×3 •× 4 Simplified Boolean function of SOP f(x₁ ‚×2 ‚׸‚ ×₁ ) = P₁ + P₁ + P₁₂ + P₁₂ 12 3' 1 2 4 • + X¸ • ×¼ + ×₁ • ×₂ • X•X + X • X•X 1 What are the the NOTS, ANDs, and ORs from the function above NOT & AND' & OR' (1's)
Simplify the following Boolean function f using K-map: m x1 x2 x3 x4 f 0 0000 1 1 0 0 0 1 1 234 10 0 0 1 0 1 0 0 1 1 X 0 1 0 0 0 5 01 0 1 0 6 0 1 1 0 1 7 0 1 1 1 0 8 1 9 1 10 1 11 12 13 0 0 0 X 001 0 1 0 1 10 110 1100 1101 0 14 1110 0 X X 15 1 1 1 10 f=Σ m(0,1,2,6,10) & don't care X=Σ m(3,8,13,14) 3- Write the function in terms of x1, x2, x3 and x4 after K-map: Σ(0, 1, 2, 6, 10) f = X • X₁₂ • X + ×₁ • x₂ 3 X ׸ • × + ×₁ • X₂ •×3 •× 4 Simplified Boolean function of SOP f(x₁ ‚×2 ‚׸‚ ×₁ ) = P₁ + P₁ + P₁₂ + P₁₂ 12 3' 1 2 4 • + X¸ • ×¼ + ×₁ • ×₂ • X•X + X • X•X 1 What are the the NOTS, ANDs, and ORs from the function above NOT & AND' & OR' (1's)
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I need help with this problem and an explanation for the solution described below. (Fundamentals of Computer Engineering: Numbering System - Adder/ Karnaugh Map)
I need to find the NOTs, ANDs, and ORs (Highlighted in yellow) from both functions written below:
Transcribed Image Text:Simplify the following Boolean function f using K-map:
m
x1
x2 x3 x4
f
0
0000
1
1
0 0 0 1
1
234 10
0
0
1
0
1
0
0
1
1
X
0
1
0
0
0
5
01
0
1
0
6
0
1
1
0
1
7
0
1
1
1
0
8
1
9
1
10
1
11
12
13
0 0 0 X
001
0 1 0 1
10 110
1100
1101
0
14
1110
0
X
X
15
1 1 1 10
f=Σ m(0,1,2,6,10) & don't care X=Σ m(3,8,13,14)
Transcribed Image Text:3- Write the function in terms of x1, x2, x3 and x4 after K-map:
Σ(0, 1, 2, 6, 10)
f = X
• X₁₂ • X
+ ×₁ • x₂
3
X
׸ • × + ×₁ • X₂ •×3 •× 4
Simplified Boolean function of SOP
f(x₁ ‚×2 ‚׸‚ ×₁ ) = P₁ + P₁ + P₁₂ + P₁₂
12 3'
1
2
4
•
+ X¸ • ×¼ + ×₁ • ×₂
•
X•X + X • X•X
1
What are the the NOTS, ANDs, and ORs from the function above
NOT &
AND' &
OR' (1's)
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