Number Representation
1. 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
r
2
’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 = 2
50
, 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
a. (12 pts) Convert the following from their initial radix to the other two common radices:
0b01011100, 0x123A, 221, 0b11011001, 0xC16F, 43
b. (12 pts) Write the following using IEC prefixes: 213
, 223
, 251
, 272
, 226
, 244
c. (12 pts) Write the following using SI prefixes: 107
, 1017
, 1011
, 1022
, 1026
, 1015
d. (6 pts) Write the following with powers of 10: 70 K, 100 E, 21 G
e. (6 pts) Write the following with powers of 2: 7 Mi, 6 Ei, 24 Ki
