VIII) Find(i)100111010.110102 + 10011111.1010112

Answered: Find (i) 100111010.110102 +…

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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Question

VIII) Find
(i)
100111010.110102 + 10011111.1010112

Expert Solution

Step 1

The given numbers are in binary, the decimal representation of the above number is,

$A = {(100111010.11010)}_{2} = (1 \times 2^{8}) + (0 \times 2^{7}) + (0 \times 2^{6}) + (1 \times 2^{5}) + (1 \times 2^{4}) + (1 \times 2^{3}) + (0 \times 2^{2}) + (1 \times 2^{1}) + (0 \times 2^{0}) + (1 \times 2^{- 1}) + (1 \times 2^{- 2}) + (0 \times 2^{- 3}) + (1 \times 2^{- 4}) + (0 \times 2^{- 5}) A = {(100111010.11010)}_{2} = 256 + 0 + 0 + 32 + 16 + 8 + 0 + 2 + 0 + 0.5 + 0.25 + 0 + 0.0625 + 0 A = {(100111010.11010)}_{2} = {(314.8125)}_{10} B = {(10011111.101011)}_{2} = (1 \times 2^{7}) + (0 \times 2^{6}) + (0 \times 2^{5}) + (1 \times 2^{4}) + (1 \times 2^{3}) + (1 \times 2^{2}) (1 \times 2^{1}) + (1 \times 2^{0}) + (1 \times 2^{- 1}) + (0 \times 2^{- 2}) + (1 \times 2^{- 3}) + (0 \times 2^{- 4}) + (1 \times 2^{- 5}) + (1 \times 2^{- 6}) B = {(10011111.101011)}_{2} = 128 + 0 + + 0 + 16 + 8 + 4 + 2 + 1 + 0.5 + 0 + 0.125 + 0 + 0.03125 + 0.015625 B = {(10011111.101011)}_{2} = {(159.671875)}_{10}$