Module 02

Arithmetic

Bitcoin Script can do basic math on stack items — addition, subtraction, comparison, and more. The inputs and outputs are all CScriptNum: a compact variable-length integer encoding specific to Bitcoin.

0 / 4 sections

What you'll learn

→Decode and encode CScriptNum integers
→Apply OP_ADD, OP_SUB, OP_ABS, OP_NEGATE, OP_MIN, OP_MAX
→Use OP_WITHIN to perform range checks
→Understand why Script integers are limited to 4 bytes

Add and subtract

OP_ADD pops the top two items, adds them, and pushes the result. OP_SUB subtracts the top from the second-to-top (second − top). Both opcodes consume their inputs — nothing is preserved.

OP_ADD

Pops two items, pushes their sum. Here 3 + 4 = 7.

Script

▶OP_3

OP_4

OP_ADD

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_3—Pushes the number 3 onto the stack.

0 stepsReady

OP_SUB

Pops two items, pushes second − top. Here 9 − 4 = 5.

Script

▶OP_9

OP_4

OP_SUB

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_9—Pushes the number 9 onto the stack.

0 stepsReady

Both operands must fit in 4 bytes (≤ 2 147 483 647). Larger inputs throw a ScriptNumError. All arithmetic operands use CScriptNum encoding.

✦Real Bitcoin

Why 4-byte integers?

Script was designed for compact transaction scripts, not general computation. 4 bytes (±2 billion) is enough for amounts, counters, and indices while keeping the script bytecode small and the consensus rules simple.

Shortcuts and signs

Several opcodes modify the top item in-place without needing a second operand.

OP_1ADD

Adds 1 to the top item. Cheaper than pushing OP_1 and calling OP_ADD.

Script

▶OP_5

OP_1ADD

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_5—Pushes the number 5 onto the stack.

0 stepsReady

OP_1SUB

Subtracts 1 from the top item.

Script

▶OP_5

OP_1SUB

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_5—Pushes the number 5 onto the stack.

0 stepsReady

OP_NEGATE

Flips the sign. Positive becomes negative and vice versa.

Script

▶OP_7

OP_NEGATE

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_7—Pushes the number 7 onto the stack.

0 stepsReady

OP_ABS

Returns the absolute value. Negative numbers become positive.

Script

▶OP_1NEGATE

OP_3

OP_MUL

OP_ABS

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_1NEGATE—Pushes the number −1 onto the stack.

0 stepsReady

Range operations

OP_MIN and OP_MAX return the smaller or larger of two values. OP_WITHIN checks whether a value falls in the range [min, max).

OP_MIN

Pops two items, pushes the smaller. Here min(3, 7) = 3.

Script

▶OP_3

OP_7

OP_MIN

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_3—Pushes the number 3 onto the stack.

0 stepsReady

OP_MAX

Pops two items, pushes the larger. Here max(3, 7) = 7.

Script

▶OP_3

OP_7

OP_MAX

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_3—Pushes the number 3 onto the stack.

0 stepsReady

OP_WITHIN

Pushes 1 if value is in [min, max), else 0. Stack order: value, min, max. Here 1 ≤ 5 < 10 → true.

Script

▶OP_5

OP_1

OP_10

OP_WITHIN

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_5—Pushes the number 5 onto the stack.

0 stepsReady

Try it yourself — what does OP_10 OP_1 OP_10 OP_WITHIN return? The upper bound is exclusive.

Ctrl+Enter to run

Script

▶OP_10

OP_1

OP_10

OP_WITHIN

Stack0 items

↑ top of stack

nothing here yet

press Step or Run to push an item

bottom

OP_10—Pushes the number 10 onto the stack.

0 stepsReady

Your turn

Use arithmetic to hit a specific target.

Challenge

Leave 21 on the stack

Write any script that leaves exactly the number 21 as the sole item on the stack. There are many valid solutions.

Ctrl+Enter to check

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