Time and frequency units

Also called: nanosecond, picosecond, megahertz, gigahertz, hertz, ns, ps, MHz, GHz, Hz

The prefixed units used in timing work: ns (10⁻⁹ s) and ps (10⁻¹² s) for delays, MHz (10⁶ Hz) and GHz (10⁹ Hz) for clocks.

Digital timing deals in very small times and very large rates, so the numbers almost always carry a prefix:

1 μs (microsecond) = 10⁻⁶ s
1 ns (nanosecond) = 10⁻⁹ s = 1000 ps
1 ps (picosecond) = 10⁻¹² s
1 Hz (hertz) = 1 cycle per second
1 MHz = 10⁶ Hz; 1 GHz = 10⁹ Hz = 1000 MHz

Period and frequency are reciprocals, f = 1 / T, and the prefixes pair up neatly:

1 μs ↔ 1 MHz
1 ns ↔ 1 GHz
1 ps ↔ 1000 GHz

Shortcuts worth memorizing: f in MHz = 1000 ÷ (T in ns), and T in ns = 1000 ÷ (f in MHz).

If you're ever unsure, write every value as a number times a power of ten, do the arithmetic, and rename the power at the end. Then sanity-check: gate delays are tens to hundreds of ps, and clocks run at MHz to a few GHz. A faster clock always has a shorter period. See clock period and clock frequency.

Worked examples

Example

Converting both ways

Find the frequency of a 2.5 ns clock, and the period of an 800 MHz clock.

1.
2.5 ns: f = 1000 ÷ 2.5 = 400 MHz. Long way: 1 ÷ (2.5 × 10⁻⁹ s) = 0.4 × 10⁹ Hz = 400 × 10⁶ Hz.
2.
800 MHz: T = 1000 ÷ 800 = 1.25 ns = 1250 ps.
3.
Check: 2.5 ns × 400 MHz = 2.5 × 10⁻⁹ × 4 × 10⁸ = 1. Period times frequency is always 1.

Example

Adding mixed units

A path has delays of 0.45 ns, 180 ps and 75 ps. What's the total?

1.
Convert to ps: 0.45 ns = 450 ps.
2.
450 + 180 + 75 = 705 ps = 0.705 ns.

Common mistakes

Dropping the prefix: 1 ÷ 4 ns is 0.25 GHz, not 0.25 Hz.
Adding ns and ps values directly without converting.
Using the MHz number as the period in ns. 50 MHz is 20 ns, not 50 ns.

Practice Time and frequency units

Interactive questions with instant feedback and a worked solution for every wrong answer.

Memory lesson full course

Which statement about the unit KiB is correct?

Timing and Sequential Logic lesson full course

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Learn it step by step

Time and frequency units is taught in Timing and Sequential Logic and Basic CPU / Computer Architecture.

Timing and Sequential Logic →Basic CPU / Computer Architecture →

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