Page 34 - ARM 64 Bit Assembly Language

Introduction 17

Example 6. Conversion from binary to decimal.

1. If the most significant bit is ‘1’, then
a. Find the two’s complement
b. Convert the result to base 10
c. Add a negative sign
2. else
a. Convert the result to base 10

Number one’s Complement two’s Complement Base 10 Negative
11010010 00101101 00101110 46 −46
1111111100010110 0000000011101001 0000000011101010 234 −234
01110100 Not negative 116
1000001101010110 0111110010101001 0111110010101010 31914 −31914
0101001111011011 Not negative 21467

Example 7. Conversion from decimal to binary.

1. Remove the negative sign
2. Convert the number to binary
3. Take the two’s complement

Base 10 Positive Binary one’s Complement two’s Complement
−46 00101110 11010001 11010010
−234 0000000011101010 1111111100010101 1111111100010110
−116 01110100 10001011 10001100
−31914 0111110010101010 1000001101010110 1000001101010111
−21467 0101001111011011 1010110000100100 1010110000100101

Subtraction using complements

One very useful feature of complement notation is that it can be used to perform subtraction
by using addition. Given two numbers in base b, x b and y b , the difference can be computed
as:

z b = x b − y b (1.2)
n
= x b + (b − y b ) − b n (1.3)
n
= x b + C(y b ) − b , (1.4)

where C(y b ) is the radix complement of y b . Assume that x b and y b , both positive and y b ≤ x b
and both numbers have the same number of digits n (y b may have leading zeros). In this case,