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Expert-verified Found in: Page 255 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # Explain how to convert from binary to base 64 expansions and from base 64 expansions to binary expansions and from octal to base 64 expansions and from base 64 expansions to octal expansions.

The base 64 expansion is the sequence of the base 64 digits corresponding to the

groups of 6 binary digits( in the same order as the order of the groups of 6 binary

digits).

The binary expansion is the sequence of the groups of binary digits corresponding to

each digit in the base 64 expansion(in the same order as the order of the

base 64 expansion)

The base 64 expansion is the sequence of the base 64 digits corresponding to the

groups of 2 octal digits( in the same order as the order of the groups of 2 octal

digits).

The octal expansion is the sequence of the groups of octal digits corresponding to

each digit in the base 64 expansion(in the same order as the order of the

base 64 expansion)

See the step by step solution

## Step 1

Binary to base 64 expansion

${2}^{6}=64$

Step 1 divide the digits of the binary expansion in group of 6 (add leading O's until

The first group contains 6 digits, if necessary).

Step 2 determine the base 64 digit that corresponds with each group of 6 binary

Digits. Step 3 the base 64 expansion is then the sequence of the base 64 digits obtain in

Step 2(in the same order as the order of the groups of 6 binary digits).

## Step 2

Base 64 to binary expansion

${2}^{6}=64$

Step 1 determine the group of 6 binary Digits corresponding to each base 64 digits. Step 2 the binary expansion is then the sequence of the groups of binary digits

obtain in Step 2(in the same order as the order of the groups of 6 binary digits).

## Step 3

$\mathbf{Octal}\mathbf{}\mathbf{to}\mathbf{}\mathbf{base}\mathbf{}\mathbf{64}\mathbf{}\mathbf{expansion}$

${8}^{6}=64$

Step 1 divide the digits of the octal expansion in group of 6 (add leading O's until

The first group contains 2 digits, if necessary).

Step 2 determine the base 64 digit that corresponds with each group of 8 binary

Digits. Step 3 the base 64 expansion is then the sequence of the base 64 digits obtain in

Step 2(in the same order as the order of the groups of 2 octal digits).

## Step 4

Base 64 to octal expansion

${8}^{2}=64$

Step 1 determine the group of 2 octal Digits corresponding to each base 64 digits. Step 2 the octal expansion is then the sequence of the groups of octal digits

obtain in Step 2(in the same order as the order of the base 64 digits). ### Want to see more solutions like these? 