What is maximum negative 8 bit binary number?

Answer 1

For unsigned maximum negative is 0.

For signed maximum negative is -128.

The answer depends on how a negative number is represented in binary. Different computers can do this differently. It also affects the maximum value of positive numbers.

An 8 bit number can have 256 combinations of 0's and 1's so it can represent 256 different values. We have different conventions for interpreting them. These conventions are built into the hardware and software of the machine.

Without recognizing negative numbers, the 256 values represent the number 0-255.

If we use signed magnitude representation, a single bit is used to determine if the number is positive or negative. The other 7 bits represent the value. 7 bits represent 127 values and a signed magnitude can have the values 0-127 as well as negative 0 to negative 127. Note that you can have both +0 and -0.

• 0 (00000000) becomes -0 (10000000),
• 5 (00000101) becomes -5 (10000101).

The largest negative number here is -127.

In 1's complement notation a number is reversed by flipping all the bits of the positive number.

• 0 (00000000) becomes -0 (11111111),
• 5 (00000101) becomes -5 (11111010).

Again we get both 0 and -0. The largest negative number here is -127

The most commonly use method in use on machines today is called 2's complement. A number is reversed by flipping all the bits and adding one: as follows:

• 1 (00000001) -> 11111110 +1 = 11111111 = -1
• -1 (11111111) -> 00000000 +1 = 00000001 = 1
• 5 (00000101) -> 11111010 +1 = 11111011 = -5
• 126 (01111110) -> 10000001 +1 = 10000010 = -126
• 127 (01111111) -> 10000000 +1 = 10000001 = -127
• -127 (10000001) -> 01111110 +1 = 01111111 = 127
• -128 (10000000) -> 01111111 +1 = 10000000 = -128 (there is no positive equivalent here of 128)
• 0 (00000000) -> 11111111 +1 = 1 00000000 = -1 (the one that is carried at the end does not fit into the 8 bit number and is lost. This is called overflow and is not regarded as an error.

2's complement arithmetic has a range of positive number 0-127 an negative 1 to negative 128. We use 10000000 as -128 because the top bit position, the 1, is already common for all the negative values. If it were a 9 bit value (01000000) it would be positive 128. It all works out great internally for the computer math processor.

The largest negative number here is -128