Why is the smallest integer for an 8 bit binary signed fixed point integer 128?

Hehe, this question is a bit interesting, the answer upstairs is completely correct, I'll explain it again, I think someone may not understand min=(10000000)b=-128 this.

max=(01111111)b=127 should be fine for everyone, the 0 in the first place here is the symbol sign, and 0 means a positive number.

And min=(10000000)b=-128 The '1' in the first digit indicates that the number is negative, and then it is puzzling:'1'Isn't it '0000000' in the back? How is it 128?

Hehe, in a computer, numbers are stored in the form of complements, the complement of positive numbers is itself, and the complements of negative numbers are: add 1 after negation. So,'000,0000'It should be in the form of a complement of a number, which is:

1000,0000" and 10000000 2 8 128

Finally this brother, sorry, you made a mistake here: "1000,0000" 10000000 2 8 128It should be 2 to the 7th power, I believe the moderator understands, I won't say it.

The largest unsigned integer that can be represented by 8 binary bits is equal to the decimal integer 255.

The binary number with no sign is represented as 00000000-111111111, which is 0-255 in decimal.

2. Binary is a number system widely used in computing technology. Binary data is a number represented by two numbers, 0 and 1. Its base is 2, the carry rule is "every two into one", and the borrowing rule is "borrow one as two".

3. Binary to decimal: From right to left, use each number of binary to multiply by the corresponding power of 2.

Binary 11111111 = 1*2 7+1*2 6+1*2 5+??1*2^0=128+64+32+16+8+4+2+1=255

So an 8-bit unsigned binary number represents a decimal number from 0-255, for a total of 256 numbers.

The 8-bit binary code is represented in the range of -127 +127

The 8-bit inverse binary code is represented in the range of -127 +127

The 8-bit complement can be represented in the range of -128 +127

N-bit binary source code and n-bit binary inverse code: -2 (n-1)-1 +2 (n-1)-1;N-bit complement: -2 (n-1) +2 (n-1)-1.

All numbers in the computer are represented by 0,1 encoding, and the plus and minus signs of numbers are no exception, if a machine digit is n digits long, it is agreed that the leftmost digit is used as the sign bit, and the remaining n-1 bits are used to represent the numeric value.

Used on the symbol bit"0"denotes a positive number; with"1"Indicates a negative number. Numeric bits represent the absolute value of the truth value. Where there are less than n-1 digits, the decimal is added to the right of the lowest digit; The integer is added to the left of the highest digit to make up the n-1 digit.

This form of computer encoding is called the original code.

Write as x=[x] original. For example, in a machine with a word length n=8:

Decimal: [original=.]

原=Integer: [1011]原=00001011

1011] original = 10001011

** in the decimal point".It was added for clarity during writing, and did not appear in the machine.

2 to the 8th power, a total of 256 digits, so the unsigned integer 0 255, the signed integer -128 127

If 0 is included, it is from 0 255

The range of unsigned integers that can be represented by 8-bit binary is 0 255;The range of signed integers that can be represented by 8-bit binary is -128 127.

Unsigned integers vs. signed integers:

1. Unsigned integers.

An unsigned number is relative to a signed number, which means that all binary bits of the entire machine word length represent numeric bits, which are equivalent to the absolute value of the number.

The highest digit of the binary number is used to represent the symbol, the highest digit is 0, which indicates a positive number, and the highest digit is 1, which indicates a negative number. This statement is true in itself, but if it is not followed, then it is false. At least it doesn't explain why the -1 of the character type is represented in binary as "1111 1111" (16decimal ff); And not "1000 0001", which we can better understand.

2. Signed integers.

Signed integers can represent positive integers, 0s, and negative integer values. Its binary encoding consists of sign bits and truth fields. Let's take 8 bits of storage space as an example, the leftmost 1 bit is the sign bit, and the remaining 7 bits are the true value range, so the range of values that can be represented is the corresponding two's complement encoding.

The representation range of the 8-bit binary original code: -127 +1278-bit binary inverse code: -127 +1278-bit binary complement representation range:

128 +127 n-bit binary source code and n-bit binary inverse code: -2 (n-1)-1 +2 (n-1)-1;N-bit complement: -2 (n-1) +2 (n-1)-1.

- Because the highest 8-bit binary code is the sign bit, so only the lower 7 bits represent the numeric value, and the highest bit represents the symbol, then the maximum value is 2 7-1 = 127, and the negative number is -127, so the eight-bit binary original code represents the integer range of -127 +127

You just have to write out the corresponding binary to know the result. Since it is said to be a range, it must be a signed bit, the highest bit is 0, 1 represents positive and negative numbers, and the rest are 1, that is, the range represented by the 8-bit binary original code, that is.

But if it's a complement, it's not in this range.,It should be -128 +127.,The calculation principle is the same.,It's just that the number is represented different.,If you're interested, you can calculate it.。

Unsigned 8 bits.

Signed 8 bits.

The largest unsigned integer that can be represented by an 8-bit binary number is equal to a decimal integer ( .

Correct Answer: a

Unsigned binary numbers are all 1 when the value is maximum, and the maximum value is 2 8-1 = 255.