answer:

explanation:

in mathematics, positive numbers (including zero) are represented as unsigned numbers. that is we do not put the +ve sign in front of them to show that are positive numbers.

however, when dealing with negative numbers we do use a -ve sign in front of the number to show that the number is negative in value and different from a positive unsigned value, and the same is true with signed binary numbers.

however, in digital circuits there is no provision made to put a plus or even a minus sign to a number, since digital systems operate with binary numbers that are represented in terms of “0’s” and “1’s”. when used together in microelectronics, these “1’s” and “0’s”, called a bit (being a contraction of binary digit), fall into several range sizes of numbers are referred to by common names, such as a byte or a word.

we have also seen previously that an 8-bit binary number (a byte) can have a value ranging from 0 (2) to 255 (2), that is 28 = 256 different combinations of bits forming a single 8-bit byte. so for example an unsigned binary number such as: 010011012 = 64 + 8 + 4 + 1 = 7710 in decimal. but digital systems and computers must also be able to use and to manipulate negative numbers as well as positive numbers.

mathematical numbers are generally made up of a sign and a value (magnitude) in the sign indicates whether the number is positive, ( + ) or negative, ( – ) with the value indicating the size of the number, for example 23, +156 or -274. presenting numbers is is called “sign-magnitude” representation since the left most digit can be used to indicate the sign and the remaining digits the magnitude or value of the number.

sign-magnitude notation is the simplest and one of the most common methods of representing positive and negative numbers either side of zero, (0). thus negative numbers are obtained simply by changing the sign of the corresponding positive number as each positive or unsigned number will have a signed opposite, for example, +2 and -2, +10 and -10, etc.

but how do we represent signed binary numbers if all we have is a bunch of one’s and zero’s. we know that binary digits, or bits only have two values, either a “1” or a “0” and conveniently for us, a sign also has only two values, being a “+” or a “–“.

then we can use a single bit to identify the sign of a signed binary number as being positive or negative in value. so to represent a positive binary number (+n) and a negative (-n) binary number, we can use them with the addition of a sign.

for signed binary numbers the most significant bit (msb) is used as the sign bit. if the sign bit is “0”, means the number is positive in value. if the sign bit is “1”, then the number is negative in value. the remaining bits in the number are used to represent the magnitude of the binary number in the usual unsigned binary number format way.

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