How to Convert Binary to Hexadecimal by Hand

To convert binary to hexadecimal, split the binary number into groups of 4 bits from the right, then replace each group with its hex digit — 1011 0111 becomes B7. Because 16 is 2⁴, every 4-bit chunk maps to exactly one hex digit. Try it in our free number base converter; the 4-bit table and worked examples are below.

The 4-bit grouping method: the only technique you need

Forget converting through decimal — the direct method is faster and less error-prone. Step 1: starting from the rightmost bit, split the binary number into groups of four. Step 2: if the leftmost group has fewer than four bits, pad it with leading zeros. Step 3: replace each 4-bit group with its single hex digit using the table below. That is the entire method. Example: 10110111 splits into 1011 and 0111; 1011 is B, 0111 is 7, so the answer is B7. The method works because each hex digit represents exactly 16 values (0–F), and 16 = 2⁴ — so every block of four binary digits corresponds to exactly one hex digit, with no overlap and no gaps. No multiplication, no powers, no intermediate decimal — just pattern-matching against sixteen entries.

The 4-bit conversion table: 0000 to 1111

Memorize — or bookmark — these sixteen mappings. 0000 = 0, 0001 = 1, 0010 = 2, 0011 = 3, 0100 = 4, 0101 = 5, 0110 = 6, 0111 = 7, 1000 = 8, 1001 = 9, 1010 = A, 1011 = B, 1100 = C, 1101 = D, 1110 = E, 1111 = F. Two memory hooks make the table stick. First, 0–9 are just the binary counting you already know — 0101 is 5, 1001 is 9, exactly as place value says. Second, A–F continue the sequence: A is 10, B is 11, up to F is 15 — and notice the top bit: every group from 1000 up has its leftmost bit set, which is why A–F all start with 1 in binary. With practice you stop consulting the table: 1100 'looks like' 12, which is C; 1010 'looks like' 10, which is A. Until then, keep the table open beside your work — even professionals glance at it for the letter digits.

Worked examples: B7, F0A, and a 32-bit address

Example 1 — 10110111: group from the right: 1011 | 0111 → B | 7 → B7. Example 2 — 111100001010: twelve bits divide evenly into three groups: 1111 | 0000 | 1010 → F | 0 | A → F0A. Example 3 — 110101 (6 bits): group from the right: 11 | 0101 — the left group is short, so pad it: 0011 | 0101 → 3 | 5 → 35. Example 4 — a 32-bit value, 11000000101010000000000000000001: eight groups of four: 1100 | 0000 | 1010 | 1000 | 0000 | 0000 | 0000 | 0001 → C | 0 | A | 8 | 0 | 0 | 0 | 1 → C0A80001 — which networking people will recognize as 192.168.0.1, the most common home-router address. Notice how the grouping method scales effortlessly: a 32-bit conversion is eight table lookups, while the via-decimal route would need you to compute a ten-digit number first.

Padding: what to do when the bits don't divide by 4

Binary numbers rarely arrive in multiples of four bits, so padding is part of the method, not an edge case. The rule: pad the leftmost group with leading zeros until it has four bits. Leading zeros never change a number's value — 11 and 0011 are both three — so padding is always safe. Pad on the left only; padding on the right multiplies the value by powers of two (appending a zero doubles a binary number). Three worked paddings: 101 → 0101 → 5. 11010 → 0001 | 1010 → 1A. 1 → 0001 → 1. The most common beginner error is grouping from the left instead of the right: 110101 grouped left-to-right as 1101 | 01 (padded 0101) gives D5 — wrong. Grouped right-to-left as 11 | 0101 (padded 0011) gives 35 — right. Always start from the rightmost bit. The rightmost bit is the ones place in every base, so right-anchored grouping preserves every digit's positional value.

Why binary and hex are natural partners

The pairing is mathematical, not conventional. A single hex digit holds exactly 16 values; four binary digits hold exactly 16 values (2⁴); therefore one hex digit and four bits carry identical information. That is why the conversion is a pure regrouping with no arithmetic — unlike binary-to-decimal, which requires multiplying by powers of two (our binary-to-decimal guide covers that method). The same logic explains why octal (base 8 = 2³) groups bits in threes — see our octal-to-decimal guide — and why there is no equally clean binary-to-decimal shortcut: 10 is not a power of 2, so decimal digits and bit groups never align. Hex won over octal historically because bytes are 8 bits — exactly two hex digits, but a fractional 2⅔ octal digits — so hex describes whole bytes cleanly. Two hex digits = one byte, always.

Binary to hex converter: the 10-second method

By hand builds understanding; a tool builds speed. Paste any binary string into our free number base converter and it returns the hex instantly — along with decimal and octal, so you can cross-check. Use the tool when the bit string is long (32+ bits), when accuracy matters more than practice (config files, exam answers you are verifying), or when you are converting from hex back to binary and want the reverse direction. The by-hand method stays valuable for three situations: technical interviews (where 'convert 10110111 to hex' is a classic five-second filter), exams that forbid tools, and debugging — when you can read hex fluently, a memory dump stops being alphabet soup and starts being data. Learn the method here, then let the tool carry the daily load.

Hex in the real world: colors, memory, and MAC addresses

Hex is the native language of computing's surfaces. Color codes: #FF5733 is three bytes — FF red, 57 green, 33 blue — and our RGB-to-hex guide shows the conversion both ways. Memory addresses: debuggers show addresses like 0x7FFF5DAB because 8 hex digits display a 32-bit address with zero waste. MAC addresses: 00:1A:2B:3C:4D:5E is six bytes in hex, the hardware fingerprint of every network card. Storage math: a megabyte is 2²⁰ bytes = 1,048,576 — a power of two, which is exactly why binary and hex thinking dominates storage; when you need the decimal answer for a drive or a download, our gigabytes to megabytes converter does the powers-of-two arithmetic for you. Unicode: U+1F600 (😀) identifies emoji by hex code point. Every one of these is binary wearing a hex costume — and now you can see through the costume.

The slower route via decimal — and why to skip it

The textbook alternative converts binary → decimal → hex: first expand by powers of two, then repeatedly divide by 16. For 10110111: the decimal value is 183, then 183 ÷ 16 = 11 remainder 7 → B7. It works, and it is worth knowing that it exists — our guides on hex-to-decimal and decimal-to-hex cover each leg. But it is strictly worse for this direction: two conversions instead of one, real arithmetic instead of table lookup, and two chances to slip instead of one. The via-decimal route made sense before the grouping method was taught widely; today it survives mainly in curricula that introduce bases in decimal-first order. Learn it for completeness, use grouping for everything else — and when in doubt, verify by hand one way and check with our free number base converter the other. Two methods agreeing is the definition of a confirmed answer. Every base-conversion guide on this blog is indexed from the ToolNest homepage.