> ## Documentation Index > Fetch the complete documentation index at: https://docs.iotools.cloud/llms.txt > Use this file to discover all available pages before exploring further. # Multi-Base Arithmetic Calculator > Add, subtract, multiply, divide or take the modulo of two numbers written in binary, octal, decimal or hexadecimal — bases auto-detected from a 0x/0b/0o prefix. Uses BigInt for arbitrary precision and shows the result in all four bases at once, with fixed-width overflow reporting and step-by-step working. [Try Multi-Base Arithmetic Calculator in your browser →](https://iotools.cloud/tool/multi-base-arithmetic-calculator/) ## OpenAPI ````yaml https://api.iotools.cloud/v1/openapi post /v1/tool/multi-base-arithmetic-calculator openapi: 3.1.0 info: title: iotools.cloud API version: 1.0.0 description: >- Run any iotools.cloud tool over HTTP. Authenticate with `Authorization: Bearer iot_live_…`. **Only `POST /v1/tool/{slug}` costs credits.** Every GET here — the catalog, a tool's schema, your balance — is free. A tool call is charged its own weight or your plan's per-call minimum, whichever is larger; `x-iotools-credit-cost` on each operation is quoted at the free-tier minimum, and `GET /v1/tools/list` returns the exact figure for your key. `GET /v1/me/credits` reports what you have left, and `GET /v1/me/usage` reports what it went on. Failures are RFC 9457 problem documents — branch on `code`. servers: - url: https://api.iotools.cloud description: Production security: - bearerAuth: [] tags: - name: Catalog description: Find a tool and read its contract. Free. - name: Converters description: >- Convert between formats, encodings, and units — Base64, CSV and JSON, timestamps, and more. Fast, free, and processed right in your browser. - name: Formatters description: >- Format, beautify, minify, and validate code and data — JSON, HTML, CSS, SQL, and regex. Clean up messy input in one click, with nothing to upload. - name: Generators description: >- Generate exactly what you need and on demand — passwords, UUIDs, QR codes, hashes, random numbers, and more. Secure, instant, and free. - name: Calculators description: >- Crunch the numbers fast — from everyday math to specialized conversions and unit work. Free online calculators that run entirely in your browser. - name: Editors description: >- Edit and transform text, code, and images with quick, focused editors that run entirely in your browser — nothing to install, and no sign-up needed. - name: Utilities description: >- Everyday developer and web utilities — DNS and IP lookups, redirect and certificate checkers, and other quick diagnostics. Free and privacy-friendly. - name: Account description: Your key's allowance, limits and usage history. paths: /v1/tool/multi-base-arithmetic-calculator: post: tags: - Calculators summary: Multi-Base Arithmetic Calculator description: >- Add, subtract, multiply, divide or take the modulo of two numbers written in binary, octal, decimal or hexadecimal — bases auto-detected from a 0x/0b/0o prefix. Uses BigInt for arbitrary precision and shows the result in all four bases at once, with fixed-width overflow reporting and step-by-step working. [Try Multi-Base Arithmetic Calculator in your browser →](https://iotools.cloud/tool/multi-base-arithmetic-calculator/) operationId: run_multi_base_arithmetic_calculator requestBody: required: false content: application/json: schema: type: object properties: firstNumber: type: string description: First number operation: enum: - add - sub - mul - div - mod description: Operation secondNumber: type: string description: Second number bitWidth: enum: - '0' - '8' - '16' - '32' - '64' description: Bit width required: [] examples: hex_binary_0xff_0b1010: summary: Hex + binary (0xFF + 0b1010) value: firstNumber: '0xFF' operation: add secondNumber: '0b1010' bitWidth: '0' octal_binary_0o17_0b11: summary: Octal - binary (0o17 - 0b11) value: firstNumber: '0o17' operation: sub secondNumber: '0b11' bitWidth: '0' negative_result_0b1010_0xff: summary: Negative result (0b1010 - 0xFF) value: firstNumber: '0b1010' operation: sub secondNumber: '0xFF' bitWidth: '0' 8_bit_overflow_0xff_x_0xff: summary: 8-bit overflow (0xFF x 0xFF) value: firstNumber: '0xFF' operation: mul secondNumber: '0xFF' bitWidth: '8' division_with_remainder_255_0b1010: summary: Division with remainder (255 / 0b1010) value: firstNumber: '255' operation: div secondNumber: '0b1010' bitWidth: '0' responses: '200': description: Tool output content: application/json: examples: hex_binary_0xff_0b1010: summary: Hex + binary (0xFF + 0b1010) value: tool: multi-base-arithmetic-calculator tool_version: 1.0.1 outputs: resultTable: - base: Binary (2) value: '0b100001001' - base: Octal (8) value: '0o411' - base: Decimal (10) value: '265' - base: Hexadecimal (16) value: '0x109' status: Unlimited precision (BigInt) — no overflow possible. workingSteps: | Inputs: A = 255 (parsed as hexadecimal) bin: 0b1111 1111 oct: 0o377 hex: 0xFF B = 10 (parsed as binary) bin: 0b1010 oct: 0o12 hex: 0xA Operation: A + B = 265 Binary addition with column carries: carry 1 1 1 1 1 1 1 0 ----------------- 0 1 1 1 1 1 1 1 1 + 0 0 0 0 0 1 0 1 0 ----------------- = 1 0 0 0 0 1 0 0 1 credits_used: 3 credits_remaining: null octal_binary_0o17_0b11: summary: Octal - binary (0o17 - 0b11) value: tool: multi-base-arithmetic-calculator tool_version: 1.0.1 outputs: resultTable: - base: Binary (2) value: '0b1100' - base: Octal (8) value: '0o14' - base: Decimal (10) value: '12' - base: Hexadecimal (16) value: '0xC' status: Unlimited precision (BigInt) — no overflow possible. workingSteps: | Inputs: A = 15 (parsed as octal) bin: 0b1111 oct: 0o17 hex: 0xF B = 3 (parsed as binary) bin: 0b0011 oct: 0o3 hex: 0x3 Operation: A - B = 12 Binary subtraction with column borrows: borrow ------- 1 1 1 1 - 0 0 1 1 ------- = 1 1 0 0 credits_used: 3 credits_remaining: null negative_result_0b1010_0xff: summary: Negative result (0b1010 - 0xFF) value: tool: multi-base-arithmetic-calculator tool_version: 1.0.1 outputs: resultTable: - base: Binary (2) value: '-0b11110101' - base: Octal (8) value: '-0o365' - base: Decimal (10) value: '-245' - base: Hexadecimal (16) value: '-0xF5' status: Unlimited precision (BigInt) — no overflow possible. workingSteps: >- Inputs: A = 10 (parsed as binary) bin: 0b1010 oct: 0o12 hex: 0xA B = 255 (parsed as hexadecimal) bin: 0b1111 1111 oct: 0o377 hex: 0xFF Operation: A - B = -245 Borrow visualization is shown when the minuend is greater than or equal to the subtrahend. The result above uses signed arithmetic. credits_used: 3 credits_remaining: null 8_bit_overflow_0xff_x_0xff: summary: 8-bit overflow (0xFF x 0xFF) value: tool: multi-base-arithmetic-calculator tool_version: 1.0.1 outputs: resultTable: - base: Binary (2) value: '0b1111111000000001' - base: Octal (8) value: '0o177001' - base: Decimal (10) value: '65025' - base: Hexadecimal (16) value: '0xFE01' status: >- Overflow in 8-bit: 65025 fits neither signed (-128 to 127) nor unsigned (0 to 255). Wrapped two's-complement — unsigned: 1, signed: 1. workingSteps: | Inputs: A = 255 (parsed as hexadecimal) bin: 0b1111 1111 oct: 0o377 hex: 0xFF B = 255 (parsed as hexadecimal) bin: 0b1111 1111 oct: 0o377 hex: 0xFF Operation: A x B = 65025 Binary multiplication (shift-and-add): 1 1 1 1 1 1 1 1 (multiplicand = 255) x 1 1 1 1 1 1 1 1 (multiplier = 255) --------------- 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 (multiplicand << 0) 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 (multiplicand << 1) 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 (multiplicand << 2) 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 (multiplicand << 3) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 (multiplicand << 4) 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 (multiplicand << 5) 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 (multiplicand << 6) 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 (multiplicand << 7) ------------------------------- = 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 credits_used: 3 credits_remaining: null division_with_remainder_255_0b1010: summary: Division with remainder (255 / 0b1010) value: tool: multi-base-arithmetic-calculator tool_version: 1.0.1 outputs: resultTable: - base: Binary (2) value: '0b11001' - base: Octal (8) value: '0o31' - base: Decimal (10) value: '25' - base: Hexadecimal (16) value: '0x19' status: Unlimited precision (BigInt) — no overflow possible. workingSteps: | Inputs: A = 255 (parsed as decimal) bin: 0b1111 1111 oct: 0o377 hex: 0xFF B = 10 (parsed as binary) bin: 0b1010 oct: 0o12 hex: 0xA Operation: A / B = 25 Binary long division (255 / 10): step | bring | running | qBit -----+-------+-----------------+----- 1 | 1 | 1 | 0 2 | 1 | 11 | 0 3 | 1 | 111 | 0 4 | 1 | 101 | 1 5 | 1 | 1 | 1 6 | 1 | 11 | 0 7 | 1 | 111 | 0 8 | 1 | 101 | 1 quotient = 0b11001 = 25 remainder = 0b101 = 5 credits_used: 3 credits_remaining: null schema: type: object required: - tool - tool_version - outputs - credits_used - credits_remaining properties: outputs: type: object properties: resultTable: type: array description: Result items: type: object properties: base: type: string description: Base value: type: string description: Value x-iotools-columns: - base - value status: type: string description: Overflow status workingSteps: type: string description: Working steps tool: type: string description: The tool's slug, echoing the {slug} in the request path. tool_version: type: string description: Output-contract version for this tool. credits_used: type: integer description: >- Credits this call consumed, after any settlement refund. 0 when metering is disabled. credits_remaining: type: - integer - 'null' description: >- Credits left in the current monthly allowance, or null when metering is disabled. request_id: type: string description: Correlation id, also sent as x-request-id. '400': $ref: '#/components/responses/ValidationError' '401': $ref: '#/components/responses/Unauthorized' '402': $ref: '#/components/responses/InsufficientCredits' '403': $ref: '#/components/responses/ToolNotAllowed' '404': $ref: '#/components/responses/ToolNotFound' '413': $ref: '#/components/responses/PayloadTooLarge' '429': $ref: '#/components/responses/RateLimited' '500': $ref: '#/components/responses/ToolFailed' '503': $ref: '#/components/responses/ToolDisabled' security: - bearerAuth: [] components: responses: ValidationError: description: Invalid request. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/validation_error title: type: string description: Short human-readable summary of the failure. examples: - Invalid request status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - validation_error detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. fields: type: - object - string additionalProperties: type: string description: >- What failed: a map of field name → message. Absent when the body itself is malformed; a single string when the failure isn't tied to one field. example: type: https://iotools.cloud/docs/errors/validation_error title: Invalid request status: 400 code: validation_error detail: One or more inputs are invalid — see `fields`. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 fields: inputString: Required Unauthorized: description: Missing or invalid API key. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/invalid_api_key title: type: string description: Short human-readable summary of the failure. examples: - Invalid API key status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - invalid_api_key detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/invalid_api_key title: Invalid API key status: 401 code: invalid_api_key detail: 'Provide ''Authorization: Bearer ''.' request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 InsufficientCredits: description: Monthly credit allowance exhausted. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/insufficient_credits title: type: string description: Short human-readable summary of the failure. examples: - Insufficient credits status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - insufficient_credits detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. credits_used: type: integer description: Always 0 — a refused call charges nothing. credits_remaining: type: integer description: Credits left in the allowance — fewer than this call costs. example: type: https://iotools.cloud/docs/errors/insufficient_credits title: Insufficient credits status: 402 code: insufficient_credits detail: This call costs 1 credit and 0 remain in this month's allowance. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 credits_used: 0 credits_remaining: 0 ToolNotAllowed: description: Tool exists but has no API surface. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/tool_not_allowed title: type: string description: Short human-readable summary of the failure. examples: - Tool not available over the API status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - tool_not_allowed detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/tool_not_allowed title: Tool not available over the API status: 403 code: tool_not_allowed detail: >- "Background Remover" is available on iotools.cloud but has no API endpoint. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 ToolNotFound: description: No such tool. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/tool_not_found title: type: string description: Short human-readable summary of the failure. examples: - Tool not found status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - tool_not_found detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/tool_not_found title: Tool not found status: 404 code: tool_not_found detail: No tool with that slug. See GET /v1/tools/list. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 PayloadTooLarge: description: Body too large. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/payload_too_large title: type: string description: Short human-readable summary of the failure. examples: - Payload too large status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - payload_too_large detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/payload_too_large title: Payload too large status: 413 code: payload_too_large detail: Request body exceeds this tool's size limit. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 RateLimited: description: Per-minute rate limit exceeded. headers: Retry-After: description: Seconds to wait before retrying (RFC 9110 delta-seconds). schema: type: integer content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/rate_limited title: type: string description: Short human-readable summary of the failure. examples: - Rate limit exceeded status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - rate_limited detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. retry_after: type: integer description: >- Seconds until the window resets — the same value as the `Retry-After` header. example: type: https://iotools.cloud/docs/errors/rate_limited title: Rate limit exceeded status: 429 code: rate_limited detail: Too many requests. Retry in 30s. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 retry_after: 30 ToolFailed: description: Tool failed to run. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/processing_error - https://iotools.cloud/docs/errors/internal_error title: type: string description: Short human-readable summary of the failure. examples: - Tool failed to run - Internal error status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - processing_error - internal_error detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. credits_used: type: integer description: >- Always 0 on `processing_error` — a failed run is refunded, floor included. credits_remaining: type: integer description: >- Credits left after the refund. Absent when metering is disabled. example: type: https://iotools.cloud/docs/errors/processing_error title: Tool failed to run status: 500 code: processing_error detail: The tool failed to run. Please try again. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 credits_used: 0 ToolDisabled: description: Tool temporarily disabled. content: application/problem+json: schema: type: object description: >- RFC 9457 problem document, served as application/problem+json. Branch on `code`; `title` is human prose and may be reworded without notice. Some failures add extension members — `fields` on validation errors, `retry_after` on 429s, `credits_used`/`credits_remaining` on billing-adjacent failures — documented on the responses that carry them. required: - type - title - status - code properties: type: type: string format: uri description: Stable documentation URI for this failure. examples: - https://iotools.cloud/docs/errors/tool_disabled - https://iotools.cloud/docs/errors/api_unconfigured title: type: string description: Short human-readable summary of the failure. examples: - Tool temporarily disabled - API not configured status: type: integer description: HTTP status code, matching the response's own status. code: type: string description: >- Stable machine-readable error code — branch on this, not `title`. enum: - tool_disabled - api_unconfigured detail: type: string description: Human explanation of this occurrence. request_id: type: string description: Correlation id, also sent as x-request-id. example: type: https://iotools.cloud/docs/errors/tool_disabled title: Tool temporarily disabled status: 503 code: tool_disabled detail: This tool is temporarily unavailable. Try again shortly. request_id: e4042b29-8f1e-4c7a-9b52-6f0d1a3c7e11 securitySchemes: bearerAuth: type: http scheme: bearer bearerFormat: iot_live_… ````