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Building a simple adder circuit Suppose we want to build a circuit that adds two 2-bit integers, x (x₁x) and y (y₁yo), to compute a sum s (s₂s₁so). Basic idea: X1 0 0 0 0 0 0 0 0 Truth table: ΧΟ Y1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 Tolol 0 0 0 0 1 1 1 1 X1 Xo 1 1 0 0 1 1 У1 Yo YO 0 1 0 1 0 1 0 S2 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 S1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 SO 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 S₂ S1 So

Building a simple adder circuit Suppose we want to build a circuit that adds two 2-bit integers, x (x₁x) and y (y₁yo), to compute a sum s (s₂s₁so). Basic idea: X1 0 0 0 0 0 0 0 0 Truth table: ΧΟ Y1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 Tolol 0 0 0 0 1 1 1 1 X1 Xo 1 1 0 0 1 1 У1 Yo YO 0 1 0 1 0 1 0 S2 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 S1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 SO 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 S₂ S1 So

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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# Building a Simple Adder Circuit Suppose we want to build a circuit that adds two 2-bit integers, x (\(x_1x_0\)) and y (\(y_1y_0\)), to compute a sum \(s (s_2s_1s_0)\). ### Basic Idea: The diagram shows a block representing the adder circuit. The inputs are: - \(x_1\) and \(x_0\) (bits of integer x) - \(y_1\) and \(y_0\) (bits of integer y) The outputs are: - \(s_2\), \(s_1\), and \(s_0\) (bits of the sum s) ### Truth Table: The truth table describes the output of the adder circuit for all possible inputs: | \(X_1\) | \(X_0\) | \(Y_1\) | \(Y_0\) | \(S_2\) | \(S_1\) | \(S_0\) | |--------|--------|--------|--------|--------|--------|--------| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | 0 | 1 | 0
Transcribed Image Text:# Building a Simple Adder Circuit Suppose we want to build a circuit that adds two 2-bit integers, x (\(x_1x_0\)) and y (\(y_1y_0\)), to compute a sum \(s (s_2s_1s_0)\). ### Basic Idea: The diagram shows a block representing the adder circuit. The inputs are: - \(x_1\) and \(x_0\) (bits of integer x) - \(y_1\) and \(y_0\) (bits of integer y) The outputs are: - \(s_2\), \(s_1\), and \(s_0\) (bits of the sum s) ### Truth Table: The truth table describes the output of the adder circuit for all possible inputs: | \(X_1\) | \(X_0\) | \(Y_1\) | \(Y_0\) | \(S_2\) | \(S_1\) | \(S_0\) | |--------|--------|--------|--------|--------|--------|--------| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | 0 | 1 | 0
Refer to Chapter 6 Slide 9, where we filled out the truth table for the 2-bit adder. We also wrote out a logical expression for the s0 bit, following a *sum of products* approach. For the s1 bit of the new circuit, follow the same procedure and write out the logical expression.
Transcribed Image Text:Refer to Chapter 6 Slide 9, where we filled out the truth table for the 2-bit adder. We also wrote out a logical expression for the s0 bit, following a *sum of products* approach. For the s1 bit of the new circuit, follow the same procedure and write out the logical expression.
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