Electrical Engineering

Number Representation

Unsigned Integers

If we have an n-digit unsigned numeral dn-1dn-2…d0 in radix (or base) r, then the value of that numeral is, which is basically saying that instead of a 10’s or 100’s place we have an r’s or r2’s place. For binary, decimal, and hex r equals 2, 10, and 16, respectively.

Just a reminder that in order to write down a large number, we typically use the IEC or SI prefixing system:

IEC: Ki = 210, Mi = 220, Gi = 230, Ti = 240, Pi = 250, Ei = 260, Zi = 270, Yi = 280; SI: K = 103, M = 106, G = 109, T = 1012, P = 1015, E = 1018, Z = 1021, Y = 1024.

1.1 Conversions

  1. (12 pts) Convert the following from their initial radix to the other two common radices: 0b01011100, 0x123A, 221, 0b11011001, 0xC16F, 43
  1. (12 pts) Write the following using IEC prefixes: 213, 223, 251, 272, 226, 244
  1. (12 pts) Write the following using SI prefixes: 107, 1017, 1011, 1022, 1026, 1015
  1. (6 pts) Write the following with powers of 10: 70 K, 100 E, 21 G
  2. (6 pts) Write the following with powers of 2: 7 Mi, 6 Ei, 24 Ki