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<p>Converting binary to hexadecimal and hexadecimal to binary is an easy conversion. The reason is that Base 16 (hexadecimal) is a power of Base 2 (binary). Every four binary digits (bits) are equal to one hexadecimal digit. The conversion looks like this:</p>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext"><b>Binary</b></span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext"><b>Hex</b></span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext"><b>Binary</b></span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext"><b>Hex</b></span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0000</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">0</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1000</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">8</span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0001</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">1</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1001</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">9</span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0010</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">2</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1010</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">A</span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0011</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">3</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1011</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">B</span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0100</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">4</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1100</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">C</span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0101</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">5</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1101</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">D</span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0110</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">6</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1110</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">E</span></td>
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<td colspan="1" rowspan="1" width="13%"><span class="smtext">0111</span></td>
<td colspan="1" rowspan="1" width="13%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="30%"><span class="smtext">7</span></td>
<td colspan="1" rowspan="1" width="17%"><span class="smtext">1111</span></td>
<td colspan="1" rowspan="1" width="23%"><span class="smtext">=</span></td>
<td colspan="1" rowspan="1" width="88%"><span class="smtext">F</span></td>
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<p>If there is a binary number that looks like 01011011, it is broken into two groups of four bits (work from right to left). These look like this: 0101 and 1011. When converting these two groups to hex, they look like 5 and B. So converting 01011011 to hex is 5B. To convert hex to binary do the opposite. Convert hex AC to binary. First convert hex A which is 1010 binary and then convert hex C which is 1100 binary.</p>
<p>No matter how large the binary number, the same conversion is always applied. Start from the right of the binary number and break the number into groups of four. If at the left end of the number it does not evenly fit into a group of four, add zeros to the left end until it is equal to four digits (bits). Then convert each group of four to its hex equivalent. Here is an example:</p>
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<td align="center" colspan="9" rowspan="1" width="25%"><span class="smtext">000100100010111110111110111001001</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext"><b>converts to:</b></span></td>
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<td colspan="1" rowspan="1" width="3%"><span class="smtext">0001</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">0010</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">0100</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">0101</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">1111</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">0111</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">1101</span></td>
<td colspan="1" rowspan="1" width="2%"><span class="smtext">1100</span></td>
<td colspan="1" rowspan="1" width="2%"><span class="smtext">1001</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext"><b>converts to:</b></span></td>
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<td colspan="1" rowspan="1" width="3%"><span class="smtext">1</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">2</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">4</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">5</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">F</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">7</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">D</span></td>
<td colspan="1" rowspan="1" width="2%"><span class="smtext">C</span></td>
<td colspan="1" rowspan="1" width="2%"><span class="smtext">9</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext"><b>so:</b></span></td>
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<td colspan="9" rowspan="1" width="25%"><span class="smtext">聽</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext">聽</span></td>
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<td colspan="10" rowspan="1" width="50%"><span class="smtext">000100100010111110111110111001001 Binary = 1245F7DC9 hex</span></td>
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<p>As stated before hex works in exactly the opposite way. Each hex digit converts to four binary digits (bits). For example:</p>
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<td align="center" colspan="9" rowspan="1" width="25%"><span class="smtext">AD46BF</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext"><b>converts to:</b></span></td>
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<td colspan="1" rowspan="1" width="3%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">A</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">D</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">4</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">6</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">B</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">F</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext"><b>converts to:</b></span></td>
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<td colspan="1" rowspan="1" width="3%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext"></span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">1010</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">1101</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">0100</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">0110</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">1011</span></td>
<td colspan="1" rowspan="1" width="3%"><span class="smtext">1111</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext"><b>so:</b></span></td>
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<td colspan="9" rowspan="1" width="25%"><span class="smtext">聽</span></td>
<td colspan="1" rowspan="1" width="25%"><span class="smtext">聽</span></td>
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<td colspan="10" rowspan="1" width="50%"><span class="smtext">AD46BF hex converts to 101011010100011010111111 binary</span></td>
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<p>AD46BF hex converts to 101011010100011010111111 binary</p>
<p>That is the conversion for binary to hexadecimal and from hexadecimal to binary.</p>
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