Question

answer sheets
a) Find 2’s complement of i) largest 10 bit binary number ii)(256)
b) Fynlain difforont
10
riii)(256)​

Answer 1

Answer:

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 which 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 (000000002) to 255 (111111112), 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 which 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 this fashion 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.