Binary multiplication and addition are realized by shifting binary numbers, which is equivalent to ×2. The computer calculates how many bits to shift according to the given addition formula and multiplication formula.

Extension:

1, representation of binary data

Binary data also uses the position counting method, and its bit weight is a power based on 2. For example, binary data110.11,and its weight order is 2 2, 21,2 0, 2-1,2-2. For integers with n digits and decimal digits with m digits, the binary data is expressed by the weighted coefficient expansion, which can be written as:

（a(n- 1)a(n-2)…a(-m)）2＝a(n- 1)×2^(n- 1)+a(n-2)×2^(n-2)+……+a( 1)×2^ 1+a(0)×2^0+a(- 1)×2^(- 1)+a(-2)×2^(-2)+……+a(-m)×2^(-m)

Generally, binary data can be written as: (a (n-1) a (n-2) ... a (1) a (-1) a (-2) ... a (-m)) 2.

note:

1. where aj represents the coefficient of the j-th position, which is one of 0 and 1.

2. The (n- 1) in A (n-1) is a subscript, so the input method cannot be typed, so it is enclosed in brackets to avoid confusion.

3.2 2 represents the square of 2, and so on.

Example 1 102 Write binary data11.01as a weighting coefficient.

Solution: (11.01) 2 = (1× 2 2)+(1× 21)+(/kloc)

Binary, like hexadecimal and octal, is carried by the power of two.

The basic law of arithmetic operation of binary data is very similar to that of decimal number operation. The most commonly used are addition and multiplication.

1. binary addition

There are four situations: 0+0 = 0.

0+ 1＝ 1

1+0＝ 1

1+1=10 is1

Example 1 103 Find the sum of (11) 2+(101) 2.

Solution: