TERM_DEF // MODULE_2_ARITHMETIC / CSCRIPTNUM
CSCRIPTNUM
CScriptNum. Bitcoin's variable-length signed integer encoding.
CScriptNum is the integer encoding used by Bitcoin Script for all numeric operations. Zero is encoded as the empty byte array (not 0x00). Integers use little-endian byte order with the sign bit in the high bit of the last byte. The maximum size for arithmetic opcodes is 4 bytes (±2,147,483,647). This encoding is distinct from standard two's complement.
This page sits in the Module 2 — Arithmetic section — Vocabulary introduced in the Arithmetic module. Read on for what it is, why it exists, how it works under the hood, and what to watch out for.
CScriptNum is the integer encoding used by Bitcoin Script for all numeric operations. Zero is encoded as the empty byte array (not 0x00). Integers use little-endian byte order with the sign bit in the high bit of the last byte. The maximum size for arithmetic opcodes is 4 bytes (±2,147,483,647). This encoding is distinct from standard two's complement.
This page sits in the Module 2 — Arithmetic section — Vocabulary introduced in the Arithmetic module. Read on for what it is, why it exists, how it works under the hood, and what to watch out for.
WHAT_CSCRIPTNUM_IS
CScriptNum — at a glance
MODULE 2
CScriptNum is part of Bitcoin Script, the small stack-based programming language that decides whether any given output can be spent. Bitcoin's variable-length signed integer encoding. Script is intentionally simple — no loops, no recursion, no global state — because every node/">full node must execute every script in every transaction, and any complexity becomes a denial-of-service vector.
CScriptNum is the integer encoding used by Bitcoin Script for all numeric operations. Zero is encoded as the empty byte array (not 0x00). Integers use little-endian byte order with the sign bit in the high bit of the last byte. The maximum size for arithmetic opcodes is 4 bytes (±2,147,483,647). This encoding is distinct from standard two's complement.
Why it exists
DESIGN
Bitcoin needed programmable money. A flat "pay address X" rule would have been too rigid — no multisig, no time-locks, no hashed commitments, no Lightning. Script is the answer: a tiny, deterministic, non-Turing-complete bytecode that lets coins be locked behind arbitrary spending conditions while keeping validation cheap and predictable.
HOW_IT_WORKS
Mechanism
HOW IT WORKS
Every UTXO is locked by a scriptPubKey — the output's locking script. To spend it, you provide a scriptSig (or witness) containing data that satisfies the lock. The node concatenates them, runs the combined script on a stack machine, and accepts the spend if and only if execution finishes with a single truthy value on the stack. CScriptNum contributes a specific stack effect within that process — opcodes either push, pop, copy, hash, branch, or verify, and they do so left-to-right deterministically.
1. The script is parsed into a sequence of opcodes and push-data items.
2. Execution starts with an empty stack and an empty alt-stack.
3. Each opcode runs in order — push opcodes add to the stack, others consume the top items and may push results.
4. Conditional opcodes (OP_IF/OP_NOTIF/OP_ELSE/OP_ENDIF) branch execution.
5. Final state: a single non-zero (truthy) value on top → the spend is authorised. Anything else (empty stack, false, error) → the script fails and the tx is rejected.
WORKED_EXAMPLE
A canonical P2PKH script — the most common locking script in Bitcoin
EXAMPLE
scriptPubKey (locking script — sits in the output):
OP_DUP OP_HASH160 <20-byte pubkey hash> OP_EQUALVERIFY OP_CHECKSIG
scriptSig (unlocking script — provided by the spender):
<signature> <pubkey>
Combined execution, left to right:
push signature → [sig]
push pubkey → [sig pubkey]
OP_DUP → [sig pubkey pubkey]
OP_HASH160 → [sig pubkey hash160(pubkey)]
push expected_hash → [sig pubkey hash160(pubkey) expected]
OP_EQUALVERIFY → [sig pubkey] (fails if hashes differ)
OP_CHECKSIG → [1] (true if signature is valid)
End state: single truthy value on top → spend authorised.
KEY_PROPERTIES
STACK-BASED
Every operation reads and writes the top of a single shared LIFO stack. No registers, no variables, no heap.
DETERMINISTIC
No randomness, no clocks. Every node executes the same script the same way — divergence would fork the network.
NON-TURING-COMPLETE
No loops, no recursion. Every script halts in bounded time, so validation cost is predictable.
CONSENSUS-CRITICAL
A misbehaving Script implementation forks its node off the network. The reference implementation is the de-facto spec.
COMMON_PITFALLS
Things that catch people out
PITFALLS
- OP_RETURN makes an output provably unspendable — useful for data commitments, ruinous if used accidentally.
- Several opcodes were disabled in 2010 after security incidents (OP_MUL, OP_DIV, OP_SUBSTR, …) and have never been re-enabled.
- Number encoding (CScriptNum) is sign-magnitude, not two's complement. -1 is 0x81, not 0xff — a frequent source of bugs.
- OP_CHECKMULTISIG has a historical off-by-one bug — it pops one extra dummy item from the stack. Always prefix the sigs with an OP_0.
RELATED_CONCEPTS
Other terms from Module 2 — Arithmetic — click any to read its page:
TERMINOLOGY_INDEX
TERMINOLOGY
CScriptNum
Bitcoin's variable-length signed integer encoding.
OP_ADD
Pop two numbers, push their sum.
Minimal push
Consensus rule: use the shortest encoding for a value.