Math 202
4G or Not 4G?
Prof. Kyhn
Sue Beauregard
February 25, 2015
1. Convert 100 mb/s (megabits/s) to the following units:
a) mB/s:
100 mb 1,000,000 b 1 B
1 mB
mB
×
×
×
= 12.5
s
1 mb
8 b 1,000,000 B
s
(The highlighted abbreviations cancel each other out leaving the remaining
units
𝑚𝐵
𝑠
.)
b) kB/s (kilobytes/s):
12.5 mB 1,000 kB
𝑘𝐵
×
= 12,500
s
1 mB
𝑠
c) B/s (bytes/s):
100 mb 1,2500 kB 1,000 B 12,500,000 kB
=
×
=
s
s
1B
s
d) b/s (bits/s):
100 mb 12,500,000 B 8 b 100,000,000 b
=
×
=
s
s
1B
s
2. How many times faster is a 4G phone that downloads at 100 Mb/sec compared
with the first dial-up modem commonly used a decade ago, which operated at a rate
of 56 Kb/sec?
(100 Mb×1,000,000)=100,000,000 b⁄s

100 Mb

4G is approximately 1786 𝑏⁄𝑠 times faster than dial-up.
56 Kb
= Change into bits
(5,600 Kb)×1,000)=56,000 b⁄s
≈ 1786 b⁄s
3. The Generation Partnership Project sets rates for HSPA and HSPA+. Determine
to the nearest tenth how many times faster the downlink speed is than the uplink
speed for each of the following:

HSPA (downlink)

HSPA+(downlink)
HSPA (uplink)
HSPA+ (uplink)
14.4 𝑀𝑏𝑖𝑡𝑠
=
5.76 𝑀𝑏𝑖𝑡𝑠
=
21 Mbits
11.5 Mbits
≈ 2.5𝑀𝑏𝑖𝑡𝑠 𝑓𝑎𝑠𝑡𝑒𝑟 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑.
≈ 1.8Mbits faster per second.
4. Speculate on why downlink speed is faster for cell phones than for uplink speed.

Downlink speed is faster because people in general downlink more than they
uplink!
5. How many times more speed is needed for true 4G capability of 100 Mb/s than
what some phone companies were advertising at 14.4 Mb/s?

(True 4G)
(Companies call 4G)
=
Mb
per second
Mb
14.4
per second
100
= 6.9 times more speed
6. A kilobyte might be expected to be 1000 bytes. In reality, computer capacity is
based on powers of 2. The number 1000 cannot be written as an integer power of
2; therefore, 1 KB (sometimes written as 1 binary KB, or 1 KiB) is actually 210 bytes,
which equals 1024 bytes. The terms megabyte, gigabyte, and terabyte use metric
prefixes—that is, powers of 10. Determine what power of 2 is the closest to the
following numbers:
𝑎) 220
𝑏) 230
𝑐) 240
7. The percentage error between the decimal (base-10) and the actual binary
(base-2) value of 1 KB is (210 − 102 )/210 × 100 the percentage error for the
following units: (a) 1 MB (b) 1 GB (c) 1 TB
a) 1 MB: 1 million (1 mega − unit) = (
220 − 106
) × 100 ≈ 4.6%
220
230 − 109
𝑏) 1 GB: 1 billion (1 giga − unit) = (
) × 100 ≈ 6.9%
230
240 − 1012
c) 1 TB: 1 trillion (1 tera − unit) = (
) × 100 ≈ 9.1%
240