GATE Computer Science (CS) Calculators
Calculators for the numerical questions in GATE Computer Science and IT, grouped by syllabus section, each showing its working so you can check answers to practice problems.
24 calculators · 3 converters · common conversions
Engineering Mathematics
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Permutation and Combination Calculator
nPr = n!/(n − r)!, nCr = n!/(r!(n − r)!)
nCr = nPr ÷ r!
Example: Choosing 3 items from 10: Combinations nCr = 120.
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Probability Calculator
P(A or B) = P(A) + P(B) − P(A and B)
independent: P(A and B) = P(A)P(B); P(A|B) = P(A and B)/P(B)
Example: Independent events with P(A) = 0.5 and P(B) = 0.4: P(A or B) = 0.7.
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- Bayes’ Theorem Calculator – Priors and likelihoods → total probability and posterior probabilities, with a Bayes table.
- Eigenvalue Calculator – A 2 × 2 or 3 × 3 matrix → eigenvalues (real or complex), characteristic equation, trace and determinant.
- LU Decomposition Calculator – A square matrix → lower and upper triangular factors L and U, and the determinant.
- Normal Distribution Calculator – Mean, standard deviation and bounds → normal probabilities, z-scores, density and percentiles.
Digital Logic
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K-Map Solver
F = Σm(…) + d(…) → minimal SOP / POS
Quine–McCluskey with an exact minimum cover
Example: F(A, B, C, D) = Σm(0, 1, 2, 5, 6, 7, 8, 9, 10, 14): Minimal SOP: F(A, B, C, D) = B′C′ + CD′ + A′BD.
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Number Base Converter
N = Σ dᵢ·bⁱ
integer part: repeated division; fraction: repeated multiplication by the base
Example: The decimal number 45.625: Binary = 101101.101.
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- Two’s Complement Calculator – Decimal ↔ two’s complement, one’s complement and sign-magnitude bit patterns, with hex.
- IEEE 754 Floating Point Converter – Decimal ↔ IEEE 754 32- or 64-bit pattern, with sign, exponent, mantissa and the value actually stored.
Computer Organization and Architecture
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Cache Memory Calculator
tag = address bits − log₂(sets) − log₂(block)
lines = cache ÷ block, sets = lines ÷ k
Example: A 32-bit address, 32 KB 4-way set-associative cache with 64-byte blocks: Tag bits = 19.
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Average Memory Access Time Calculator
AMAT = t₁ + (1 − h₁)[t₂ + (1 − h₂)tₘ]
hierarchical access; simultaneous: h₁t₁ + (1 − h₁)h₂t₂ + …
Example: A 1 ns cache with a 95 % hit rate in front of 100 ns memory: Average memory access time = 6 ns.
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- Pipeline Speedup Calculator – Stage delays, latch delay, instructions and stalls → clock period, execution time, speedup and efficiency.
- Amdahl’s Law Calculator – Fraction improved and its speedup → overall speedup, upper limit and efficiency.
Algorithms
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Master Theorem Calculator
T(n) = aT(n/b) + Θ(nᵏ logᵖ n)
compare k with log_b a
Example: T(n) = 8T(n/2) + n²: T(n) = Θ(n^3).
Operating Systems
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CPU Scheduling Calculator
TAT = completion − arrival, WT = TAT − burst
response = first run − arrival
Example: Four processes arriving at 0, 1, 2 and 3 with bursts 8, 4, 9 and 5 under SRTF: Average waiting time = 6.5.
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Page Replacement Calculator
hit ratio = hits ÷ references
FIFO evicts the oldest, LRU the least recently used, Optimal the one used furthest ahead
Example: The reference string 7 0 1 2 0 3 0 4 2 3 0 3 2 1 2 0 1 7 0 1 with 3 frames: Page faults = 12.
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- Disk Scheduling Calculator – Request queue, head position and direction → service order and total head movement for six algorithms.
- Banker’s Algorithm Calculator – Allocation, Max and Available → Need matrix, work trace and a safe sequence (or unsafe).
- Paging Calculator – Virtual and physical address bits, page size and PTE size → pages, frames, page table size and TLB EAT.
Computer Networks
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Subnet Calculator
network = IP AND mask, broadcast = network OR wildcard
hosts = 2^(32 − prefix) − 2
Example: 192.168.10.77/26: Network address = 192.168.10.64/26.
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CRC Calculator
frame = data · 2ʳ + (data · 2ʳ mod G)
modulo-2 (XOR) division; r = degree of G
Example: Data 1101011111 with generator x⁴ + x + 1 (10011): Transmitted frame = 11010111110010.
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- Hamming Code Calculator – Data bits → Hamming code word; or a received word → syndrome, error position and corrected data.
- Sliding Window Efficiency Calculator – Bandwidth, frame size, propagation delay and window → transmission time, efficiency, throughput and sequence bits.
Unit Converters for GATE Computer Science (CS)
- Data Storage Converter – bytes, KB, MB, GB, TB, KiB, MiB, GiB
- Data Transfer Rate Converter – Mbps, MB/s, Gbps, kbps, MiB/s
- Frequency & RPM Converter – Hz, kHz, MHz, GHz, rpm, rad/s
Common GATE Computer Science (CS) Conversions
How to use these GATE Computer Science calculators
GATE CS has many numerical answer type (NAT) questions where one arithmetic slip costs the marks: average waiting time, page faults, tag bits, page table size, subnet ranges or CRC bits. Each calculator here follows the standard textbook conventions (Silberschatz for operating systems, Tanenbaum for networks, Mano for digital logic) and shows its working.
The operating-system tools draw the Gantt chart and the frame table, the computer-organisation tools split addresses into tag, index and offset or compute pipeline timing, and the networking tools work bit by bit, from IPv4 masks to modulo-2 division. Where textbooks differ, such as counting the C-SCAN return seek, both answers are shown.
Solve the question by hand first, then enter the same numbers here to check. If your answer differs, compare the intermediate rows; most mistakes come from units (bytes versus bits), tie-breaking rules in scheduling, or forgetting to append zeros before a CRC division.