{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

20085eeM16_2_Homework2_Soln

20085eeM16_2_Homework2_Soln - 2 7-Seqment Decoder You are...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2. 7-Seqment Decoder You are designing a combinational system for displaying binary coded decimal (BCD) digits. F b a. Write down the truth table for z b = F(x b ) X 3 X 2 X 1 X 0 Z 6 Z 5 Z 4 Z 3 Z 2 Z 1 Z 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 b. Write the switching expressions for z b in a sum-of-product form. Z 6 = x3’x2’x1x0’ + x3’x2’x1x0 + x3’x2x1’x0’ + x3’x2x1’x0 + x3’x2x1x0’ + x3x2’x1’x0’ + x3x2’x1’x0 Z 5 = x3’x2’x1’x0’ + x3’x2’x1x0’ + x3’x2’x1x0 + x3’x2x1’x0 + x3’x2x1x0 + x3x2’x1’x0’ + x3x2’x1’x0 Z 4 = x3’x2’x1’x0’ + x3’x2x1’x0’ + x3’x2x1’x0 + x3’x2x1x0’ + x3x2’x1’x0’ + x3x2’x1’x0 Z 3 = x3’x2’x1’x0’ + x3’x2’x1x0’ + x3’x2x1x0’ + x3x2’x1’x0’ Z 2 = x3’x2’x1’x0’ + x3’x2’x1x0’ + x3’x2’x1x0 + x3’x2x1’x0 + x3’x2x1x0’ + x3x2’x1’x0’ Z 1 = x3’x2’x1’x0’ + x3’x2’x1’x0 + x3’x2’x1x0 + x3’x2x1’x0’ + x3’x2x1’x0 + x3’x2x1x0’ + x3’x2x1x0 + x3x2’x1’x0’ + x3x2’x1’x0 Z 0 = x3’x2’x1’x0’ + x3’x2’x1’x0 + x3’x2’x1x0’ + x3’x2’x1x0 + x3’x2x1’x0’ + x3’x2x1x0 + x3x2’x1’x0’ + x3x2’x1’x0 BCD coder 5 x b control signal decoder 4 3 6 x in {0,1,2 …,9} z b 1 0 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
c. Use Boolean algebra to minimize switching expressions. Z 6 = x3’x2’x1x0’ + x3’x2’x1x0 + x3’x2x1’x0’ + x3’x2x1’x0 + x3’x2x1x0’ + x3x2’x1’x0’ + x3x2’x1’x0 = x3’x2’x1(x0’ + x0) + x3’x2x1’(x0’ + x0) + x3’x2x1x0’ + x3x2’x1’(x0’ + x0) By Distributive = x3’x2’x1 + x3’x2x1’ + x3’x2x1x0’ + x3x2’x1’ By Complement Z 5 = x3’x2’x1’x0’ + x3’x2’x1x0’ + x3’x2’x1x0 + x3’x2x1’x0 + x3’x2x1x0 + x3x2’x1’x0’ + x3x2’x1’x0 = x3’x2’x0’(x1’ + x1) + x3’x2’x1x0 + x3’x2x0(x1’ + x1) + x3x2’x1’(x0’ + x0) By Distributive
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}