Binary to Hexadecimal Chart: Read 4 Bits at a Time

The Binary to Hexadecimal Chart Explained: Read 4 Bits at a Time

A binary to hexadecimal chart is a lookup table that pairs every 4-bit binary group (a "nibble") with its single hexadecimal digit, from 0000 = 0 up to 1111 = F. Because 4 bits map to exactly one hex digit, the chart lets you convert long strings of 1s and 0s into compact hex by reading them in tidy groups of four, without doing any arithmetic in your head.

If you only need the answer right now, the short version is this: split your binary number into 4-bit chunks starting from the right, look up each chunk in the chart, and write the matching hex digits in the same order. That is the entire method. The rest of this guide explains why it works, gives you the full reference chart, walks through worked examples, and covers the edge cases that trip people up. When you want to skip the manual lookup entirely, our free Binary to Hex converter does it instantly in your browser.

Why 4 Bits Equal 1 Hex Digit

Hexadecimal is base-16, meaning each digit can represent 16 distinct values (0 through 15, written 0-9 then A-F). Binary is base-2, where each digit (bit) holds 2 values. The magic number is 4: because 2 to the power of 4 equals 16, four binary bits can express exactly the same range as one hex digit. This clean alignment is the whole reason hex is so popular among programmers — it is a human-friendly shorthand for binary that never loses precision.

Contrast this with decimal (base-10). There is no whole number of bits that maps neatly to one decimal digit, which is why binary-to-decimal conversion requires real multiplication and addition. Binary-to-hex needs none of that. You are simply re-grouping the same bits and renaming each group.

One nibble (4 bits) = one hex digit. One byte (8 bits) = exactly two hex digits. This is why a byte like 11111111 is always written FF.

The Complete Binary to Hexadecimal Chart

Here is the full reference. Every possible 4-bit pattern appears exactly once, alongside its hex digit and decimal value. Memorize the first column or keep it bookmarked — it is all you ever need for conversion in either direction.

Notice a useful pattern in the chart: the four columns of bits represent the place values 8, 4, 2, and 1. To find the decimal value of any nibble, add up the place values wherever a 1 appears. For example, 1011 is 8 + 0 + 2 + 1 = 11, which is hex B. Once you internalize the 8-4-2-1 weights, you can rebuild the chart from memory anytime.

The 8-4-2-1 Mental Shortcut

Write the weights 8, 4, 2, 1 above your four bits. Cross out the weights under any 0. Sum what remains. That sum (0-15) is your decimal value, and you map 10-15 to A-F. This trick means you never have to memorize all 16 rows — just the four weights and the six letter mappings.

How to Read the Chart: Step by Step

Converting a full binary number to hex using the chart takes four steps. The method works for any length of binary string.

1. Group from the right. Starting at the rightmost bit, split the binary into chunks of 4. The least significant bits must stay together on the right.
2. Pad the leftmost group. If the final (leftmost) group has fewer than 4 bits, add leading zeros until it does. Leading zeros never change the value.
3. Look up each group. Find each 4-bit chunk in the chart and note its hex digit.
4. Write the hex in order. Concatenate the hex digits left to right, exactly matching the order of your binary groups.

Worked Example: Converting 110110111 to Hex

Take the 9-bit number 110110111. Following the steps:

• Group from the right into fours: 1 1011 0111.
• Pad the leftmost group from 1 to 0001. Now we have 0001 1011 0111.
• Look up each group: 0001 = 1, 1011 = B, 0111 = 7.
• Write them in order: 1B7.

So 110110111 in binary equals 1B7 in hexadecimal. To verify, you could convert both to decimal (439) and confirm they match. The grouping method is reliable as long as you always pad on the left, never the right — padding the right would shift place values and corrupt the answer.

Another Example: A Full Byte

The byte 11001010 splits cleanly into 1100 and 1010. From the chart, 1100 = C and 1010 = A, giving CA. Every 8-bit byte produces exactly two hex characters, which is why memory addresses and color codes are so compact in hex: a single byte that would take eight binary digits collapses to two.

Going the Other Way: Hex to Binary

The chart works in reverse just as easily. To expand hexadecimal back into binary, replace each hex digit with its 4-bit pattern from the chart, keeping the order. There is no grouping or padding to worry about because each hex digit always becomes exactly four bits.

One thing to watch: when expanding hex to binary you must write all four bits for every digit, including leading zeros. Writing 3 as just 11 instead of 0011 would misalign every group that follows.

Where You Will Actually Use This

The binary to hexadecimal chart is not just an academic exercise. It underpins a surprising amount of everyday computing:

• Color codes. A web color like #FF8800 is three bytes — red, green, blue — each written as two hex digits, each of which is four bits.
• Memory addresses. Debuggers and hex editors display addresses in hex because it maps cleanly to the underlying binary while staying readable.
• MAC addresses and UUIDs. Hardware identifiers are commonly shown in hex groups for the same compactness reason.
• Bit flags and masks. Engineers often define permission bits or status flags in binary, then store or transmit them in hex.

For larger or repeated conversions, doing it by hand becomes error-prone. That is exactly where our Binary to Hex converter earns its place — paste any binary string and get clean hex instantly, with no signup. You can explore more bit-level utilities in the Binary Converter hub, and if you are learning number systems from scratch, the binary alphabet guide and our decimal to hexadecimal walkthrough pair nicely with this chart.

Common Mistakes to Avoid

• Grouping from the left. Always start grouping at the rightmost bit. Grouping from the left throws off the place values of every chunk.
• Padding on the wrong side. Only the leftmost group gets zero-padded, and only on its left. Never pad the right side.
• Forgetting letters for 10-15. Values 10 through 15 become A-F, not "10", "11", and so on. Writing 1010 as "10" instead of "A" is the single most common slip.
• Dropping leading zeros in hex-to-binary. Each hex digit always expands to four bits. Skipping leading zeros breaks alignment.

Frequently Asked Questions

Why does 4 bits equal exactly one hexadecimal digit?

Because hexadecimal is base-16 and 2 raised to the 4th power equals 16. Four binary bits can represent 16 distinct values (0-15), which is precisely the range of a single hex digit (0-F). The bases line up perfectly, so no arithmetic is needed to convert.

How do I convert binary to hex without a chart?

Use the 8-4-2-1 weights. Group your binary into fours from the right, then for each group add the place values (8, 4, 2, 1) wherever a 1 appears. Map sums of 10-15 to the letters A-F. The chart simply pre-computes this for you.

What is a nibble?

A nibble is a group of 4 bits, exactly half of an 8-bit byte. The term is a playful spin on "byte." One nibble corresponds to one hex digit, which is why the binary to hexadecimal chart has 16 rows.

Do I group binary from the left or the right?

Always from the right. The rightmost bits are the least significant, so they must stay grouped together. If the leftmost group ends up short, pad it with leading zeros on its left.

How many hex digits does one byte produce?

Exactly two. A byte is 8 bits, and since 4 bits make one hex digit, 8 bits make two. That is why a full byte ranges from 00 to FF in hex.

Is hexadecimal the same data as binary?

Yes. Hex is just a more compact way to write the same bits. Converting between them never adds or loses information — you are only re-grouping and renaming, which is why the conversion is lossless and reversible.

What does the leading 0x mean in something like 0x1B7?

The 0x prefix is a convention that signals "the following digits are hexadecimal." It is not part of the value itself. 0x1B7 and 1B7 represent the same number; the prefix just prevents confusion with decimal.

Can I convert hex back to binary with the same chart?

Yes. Read the chart in reverse: replace each hex digit with its 4-bit pattern, keeping the order and always writing all four bits including leading zeros. No grouping or padding is needed because each hex digit maps to exactly four bits.