Page 29 - ARM 64 Bit Assembly Language

12 Chapter 1

Base 2 Base 16
0000 0
0001 1
0010 2
0011 3 Base 2 Base 8
0100 4 000 0
0101 5 001 1
0110 6 010 2
0111 7 011 3
1000 8 100 4
1001 9 101 5
1010 A 110 6
1011 B 111 7
1100 C
1101 D
1110 E
1111 F

Figure 1.3: Tables used for converting between binary, octal, and hexadecimal.

digit. Conversely, each hexadecimal digit can be converted to exactly four binary digits, and
each octal digit can be converted to exactly three binary digits. This relationship makes it pos-
sible to do very fast conversions using the tables shown in Fig. 1.3.

When converting from hexadecimal to binary, all that is necessary is to replace each hex digit
with the corresponding binary digits from the table. For example, to convert 5AC4 16 to bi-
nary, we just replace “5” with “0101,” replace “A” with “1010,” replace “C” with “1100,”
and replace “4” with “0100.” So, just by referring to the table, we can immediately see that
5AC4 16 = 0101101011000100 2 . This method works exactly the same for converting from
octal to binary, except that it uses the table on the right side of Fig. 1.3.

Converting from binary to hexadecimal is also very easy using the table. Given a binary
number, n, take the four least significant digits of n and find them in the table on the left
side of Fig. 1.3. The hexadecimal digit on the matching line of the table is the least signif-
icant hex digit. Repeat the process with the next set of four bits and continue until there
are no bits remaining in the binary number. For example, to convert 0011100101010111 2
to hexadecimal, just divide the number into groups of four bits, starting on the right, to
get: 0011|1001|0101|0111 2 . Now replace each group of four bits by looking up the cor-
responding hex digit in the table on the left side of Fig. 1.3, to convert the binary num-
ber to 3957 16 . In the case where the binary number does not have enough bits, simply
pad with zeros in the high-order bits. For example, dividing the number 1001100010011 2
into groups of four yields 1|0011|0001|0011 2 and padding with zeros in the high-order