Having designed a binary adder, you are now ready to design a 2-bit by 2-bit unsigned binary multiplier. The multiplier takes two 2-bit inputs A[1:0] and B[1:0] and produces an output Y, which is the product of A[1:0] and B[1:0]. The standard notation for this is: Y = A10 · B10 a. What is the maximum value that can be represented in two bits for A(A[1:0])? b. What is the maximum value that can be represented in two bits for B(B[1:0])?

Having designed a binary adder, you are now ready to design a 2-bit by 2-bit unsigned binary multiplier. The multiplier takes two 2-bit inputs A[1:0] and B[1:0] and produces an output Y, which is the product of A[1:0] and B[1:0]. The standard notation for this is: Y = A10 · B10 a. What is the maximum value that can be represented in two bits for A(A[1:0])? b. What is the maximum value that can be represented in two bits for B(B[1:0])?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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3.34 Having designed a binary adder, you are now ready to design a 2-bit by
2-bit unsigned binary multiplier. The multiplier takes two 2-bit inputs
A[1:0] and B[1:0] and produces an output Y, which is the product of
A[1:0] and B[1:0]. The standard notation for this is:
Y = A10 · B10
a. What is the maximum value that can be represented in two bits for
A(A[1:0])?
b. What is the maximum value that can be represented in two bits for
B(B[1:0])?

c. What is the maximum possible value of Y?
d. What is the number of required bits to represent the maximum value
of Y?
e. Write a truth table for the multiplier described above. You will have a
four-input truth table with the inputs being A[1], A[0], B[1], and
B[0].
f. Implement the third bit of output, Y[2] from the truth table using only
AND, OR, and NOT gates.

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