Binary numbers

Problems in Exploration Seismology and their Solutions

Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	7
Pages	221 - 252
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem

1. Express the decimal numbers 19 and 10 as binary numbers.
2. Add the binary numbers together and convert the sum to a decimal number.
3. Multiply the two binary numbers and convert the product to decimal form.

Background

Mathematical operations are carried out in binary arithmetic in the same way as in decimal arithmetic. As an example of the similarity between decimal and binary arithmetic, when we add 75 to 129, we add 9 to 5 in the right-hand column and get 4 plus 1 to be carried to the next column. In binary addition, we have only the digits 1 and 0; when we add 1 to 1 we get 0 plus 1 to carry to the next column. In subtraction, when we subtract 1 from 0 we must borrow 1 from the next nonzero column to the left. Multiplication is identical in the two systems. To express a decimal number as a binary number, we subtract the largest power of 2 that is less than the decimal number, then follow the same procedure with the remainders until we end up with 1 or 0.

Solution

1. $19=2^{4}+2^{1}+2^{0}=10011;10=2^{3}+2^{1}=1010.$
2. $10011+1010=11101=2^{4}+2^{3}+2^{2}+2^{0}=16+8+4+1=29.$
3. $10011\times 1010=$ ${\begin{array}{c}10\,011\\1\,010\\\hline 100\,110\\10\,011\,0\\\hline 10\,111\,110=2^{7}+2^{5}+2^{4}+2^{3}+2^{2}+2^{1}+0\\\qquad =128+32+16+8+4+2\\=190.\end{array}}$

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Characteristics of seismic events	Reflection field methods
Table of Contents (book)

Also in this chapter

• Radiolocation errors because of velocity variations
• Effect of station angle on location errors
• Transit satellite navigation
• Effective penetration of profiler sources
• Directivity of linear sources
• Sosie method
• Energy from an air-gun array
• Dominant frequencies of marine sources
• Effect of coil inductance on geophone equation
• Streamer feathering due to cross-currents
• Filtering effect of geophones and amplifiers
• Filter effects on waveshape
• Effect of filtering on event picking
• Binary numbers

External links

find literature about Binary numbers