8_DigitalSystemDesign

Thethirdinput thecarry inputisshowningray 01 765 915

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Unformatted text preview: h” #2 lower voltage Building Something • Let’s build an adder to add two numbers Adder • To do that, we’ll first need a building block called a full adder 19 Adding Two Numbers • Let’s think about how we add base‐10 numbers • We add numbers column by column 7 6 5 + 9 1 5 0 Adding Two Numbers • Let’s think about how we add base‐10 numbers • We addnumbers column by column • When a column’s sum is more than what one digit can represent, we carry the left digit one column to the left 1 7 6 5 + 9 1 5 0 20 Adding Two Numbers • We can think of each column as adding three numbers and having two output digits—one in each of two columns • The column adders are shown here with red, green, and blue adder blocks. The third input (the carry input) is shown in gray 0 1 7 6 5 + 9 1 5 1 6 8 0 Adding Two Binary Numbers • Binary addition is done exactly the same way but now digits are 0’s and 1’s only and a carry is generated when the sum in a column is 2 or higher • Notice again each adder block (column) has three inputs and two outputs 1 1 1 1 1 + 1 0 1 1 1 0 0 carries sums 21 A Full Adder • These adder blocks are called Full Adders and they add three binary numbers ABC Full Adder Carry-Out Sum Truth Table • How do we design a full adder? • A great thing about binary design—we can often look at every possible combination. Every combination is listed here in a Truth Table Inputs Outputs A B C Cout Sum 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 22 Digital Circuit Design • Now let’s design the circuit for Cout, one of the two outputs A B C Cout Sum 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 Digital Circuit Design • Now let’s design the circuit for Cout, one of the two outputs A B C Cout Sum • We next draw a Karnaugh 0 0 0 0 0 map, which is a truth table 0 0 1 0 1 drawn in a special way: 0 1 0 0 1 A 0 1 1 1 0 0 1 1 0 0 0 1 00 0 0 1 0 1 1 0 BC 01 0 1 1 1 0 1 0 11 1 1 1 1 1 1 1 10 0 1 23 Karnaugh Map • The Karnaugh map tells us the logic equation for Cout is, Cout = (A AND C) OR (A AND B) OR (B AND C) BC A 0 1 00 0 0 01 0 1 11 1 1 10 0 1 One Output of a Full Adder • We can draw the circuit using AND and OR blocks Cout = (A AND C) OR (A AND B) OR (B AND C) A C AND OR A B AND OR B C Car...
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This note was uploaded on 01/29/2014 for the course MAT 1 taught by Professor Higgins during the Fall '13 term at UC Davis.

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