Question

1. Suppose it's a machine that uses four bits for numeric expression. Use the remuneration of 2 to indicate negative numbers and perform the following operations.
a) -4 -3 = ?
b) 4 - 3 = ?
c) Demonstrate that ignoring end-carry is a normal calculation.
d) Repeat the overflow situation and discuss all detection methods.

Answer 1

[a]

In case of a four bit calculation, we have range from 0000 to 1111.

In digital electronics, a –ve number is represented by its 2’s complement.

Therefore, in [a] part, we have to perform (-4 – 3) computation.

To represent -4 as binary Number:

4 =                                         0 1 0 0

1’s Complkement                1 0 1 1

Add 1                                         + 1

We get, - 4) =                       1 1 0 0

3 =                                         0 0 1 1

1’s Complkement                1 1 0 0

Add 1                                         + 1

We get, - 3) =                       1 1 0 1

Now _4 – 3 = (-4) + (-3) = 1 1 0 0        

                                              1 1 0 1

We get (-7) =                        1 0 0 1

[b]

In case of a four bit calculation, we have range from 0000 to 1111.

In digital electronics, a –ve number is represented by its 2’s complement.

Therefore, in [b] part, we have to perform (4 – 3) computation.

To represent 4 as binary Number:

4 =                                         0 1 0 0

3 =                                         0 0 1 1

1’s Complkement                1 1 0 0

Add 1                                         + 1

We get, - 3) =                       1 1 0 1

Now 4 – 3 = (4) + (-3) =    0 1 0 0

                                              1 1 0 1

We get (1) =                         0 0 0 1

[c] In both case above, if we ignore the carry, we get the same results.

[d]

Over flow situation occurs when all bits are 1111.

The numbers rolls down from 1111 to 0000.

Therefore, in four bit (4-bits) representation any number greater than 15 will be rolled down to zero due to over flow.