Page 68 - Engineering Digital Design

2.5 CONVERSION BETWEEN NUMBER SYSTEMS 39

Table 2.4 Summary of recommended methods for integer conversion
by noncomputer means
Integer Conversion
Conversion Method
Radix division by radix r using Eq. (2.5)
N 10 -> N r
N s -^ NIO Eq. (2.2) or (2.3)
N s).v^]0 -+ NrWic , N, -+ JVio by Eq. (2.2) or (2.3)
NIO —* N r radix division by r using Eq. (2.5)
Special Cases for Binary Forms

N 2 -» NIO Positional weighting
N 2 -> NBCH Partition N 2 into groups of four bits starting from
radix point, then apply Table 2.3
N 2 — > NBCO Partition A^ into groups of three bits starting from
radix point, then apply Table 2.3
Reverse of N2 — > NBCH
NBCH -> N 2
Reverse of N 2 —> NBCO
NBCO -* N 2
NBCH -> NBCO NBCH -> N 2 -+ NBCO
NBCO -» NBCH NBCO -+ N 2 -+ NBCH
N fio) -> %55 Add0011 2 (=3i 0 )toN BC D
NXS^ -> NBCD Subtract 001 1 2 (= 3 10) from NXSB

Algorithm 2.2: #2* •«- N%> Positive Integer Conversion
To convert numbers A/2« to N 2k, where n and k are integers, convert the groups of n
digits in A^2« to A^, then reorganize the result in groups of k beginning with the LSB and
1
proceeding toward the MSB. Finally, replace each group of k, reading from the LSB,
with the digit appropriate for number system #2* •

The integer conversion methods of Table 2.4 and Algorithms 2.1 and 2.2 are illustrated
by the following simple examples:

EXAMPLE 2.1 139, 0 -+ N 2
N/r Q R
139/2 = 69 1
69/2 = 34 1
34/2 = 17 0
17/2 = 8 1
8/ 2 = 4 0
4/ 2 = 2 0
2/ 2 = 1 0
1/2 = 0 1 139i 0= 10001011 2

EXAMPLE 2.2 10001011 2 -> N\ 0
By positional weights N [0 = 128 + 8 + 2 + 1 = 139i 0.

Note that leading O's may be needed to complete the groups of k.