Binary Bit Weight Problem, Binary Bit Value Concept?

Generally speaking, the bit power of the binary system is the number of bits, and the binary bit power is 2.

Now to explain it to you:

For example, in two-digit binary, the lowest bit is 2 to the power of 0.

That is, 1, and the highest digit is the 1st power of 2, that is, 2;

If this binary number.

is 01, then this binary number is converted to decimal.

That's 1*1+0*2=1

If it is 10, then the conversion to decimal is 0*1+1*2=2 and for example, a three-digit binary number, the lowest bit is 2 to the power of 2, that is, 1, the higher bit is 2 to the 1st power, that is, 2, and the highest digit is 2 to the 2nd power, that is, 4

If this binary number is 101, then convert to decimal as 1*1+0*2+1*4=5, which is the bit weight, that is, each bit of the binary number is based on 2.

, and then the power starts at 0, adding 1 for each higher power

Binary data also uses position notation, and its bit weight is a power of 2. For example, binary data has weights in the order of -2. For integers with n digits, binary data with m decimal places is expressed in a weighted coefficient formula, 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)

Binary data can generally be written as: (a(n-1)a(n-2)....a(1)a(0).a(-1)a(-2)…a(-m)）2。

Hello, glad for your question. First of all, let's take the decimal system that we are more familiar with as an example. Why does the decimal 123 read one hundred and twenty-three?

Because 1 is in the hundred, 2 in the ten, and 3 in the single digit. That is, 123 = 1 * 100 + 2 * 10 + 3 * 1, where the sum of 1 is the bit weight of the hundred, ten and single digits respectively. It can be seen that the weight of the nth bit of the integer part is the n-1 power of 10, and so on, the weight of the mth bit of the decimal part is the -m power of 10.

Then for binary, the bit weight of the nth bit of the integer part is the n-1 power of 2, and the bit weight of the mth bit of the decimal part is the -m power of 2.

From the lowest (far right) digit, the digits on the bits are multiplied by the weight of the base, and the weight is the digit of 2 minus one digit.

For example, the second digit is the (2-1) square of 2, which is 2;The 8th position is 2 (8-1) to the power of 128. Add up all the values.

2 (1-1) represents 2 to the power of 0, which is 1;Other analogies.

For example, binary 1101 is converted to decimal: 1*2(1-1)+0*2(2-1)+1*2(3-1)+1*2(4-1)=1+0+4+8=13.

Based on one digit to the left of the decimal point, its weight is 1, and to the left, in order of ,...

Starting from the decimal point, the weight of each person to the right is 16, 1 and 32 ,......

The digit weight is the (digit -1) of the base system, and the value of the n-th digit is equal to the number multiplied by the n-1 power of the base system.

For example, the weight of the 4th digit 1 of the decimal number 1462 is 1 10 3, which is 1000, and the decimal weight is 2 (n-1), for example, 1000, the weight of the 4th digit 1 is 1 2 3=8

1. In various number systems (whether binary, decimal, hexadecimal, etc.), the size of the value represented by each number is not only related to the size of the special number itself, but also related to the position of the number.

2. Take the decimal system as an unscientific but most popular analogy, you can't say that 4 is necessarily bigger than 2, but also depends on its position in the whole number. For example, 4 in 40 represents a smaller value than 2 in 200.

Integer. Binary bit weight 2 to the nth power starts from right to left 0.

Decimal fraction. Binary bitweights of 2 to the -n power start from left to right -1.

In computer memory, a byte is made up of (8) binary bits.

The symbol for an integer less than 2 in a binary notation system is generally represented by 1 or 0, which is one of two states with equal probability.

The number of binary bits can represent the length of a machine word, and the amount of information contained in a binary bit is called one bit.