Digital Systems ad Binary numbers

Question 1

Binary Addition:

of signed binary.

Answer 1

The addition of two signed binary numbers with negative numbers represented in
signed‐2’s‐complement form is obtained from the addition of the two numbers, including their sign bits. A carry out of the sign‐bit position is discarded.

Note that negative numbers must be initially in 2’s‐complement form and that if the sum
obtained after the addition is negative, it is in 2’s‐complement form.

Question 2

Subtraction of two signed binary numbers when negative numbers are in 2’s‐complement
form

Answer 2

Take the 2’s complement of the subtrahend (including the sign bit) and add it to the
minuend (including the sign bit). A carry out of the sign‐bit position is discarded.

Question 3

Circuits for these arithmetic:

Answer 3

It is worth noting that binary numbers in the signed‐complement system are added
and subtracted by the same basic addition and subtraction rules as unsigned numbers.
Therefore, computers need only one common hardware circuit to handle both types of
arithmetic . This consideration has resulted in the signed‐complement system being used
in virtually all arithmetic units of computer systems. The user or programmer must
interpret the results of such addition or subtraction differently, depending on whether
it is assumed that the numbers are signed or unsigned.

Question 4

BCD and it’s relationship with decimals and binary. It’s more closer to or equivalent to?

Answer 4

It is important to realize that BCD numbers are decimal numbers and not binary
numbers, although they use bits in their representation. The only difference between a
decimal number and BCD is that decimals are written with the symbols 0, 1, 2, c, 9
and BCD numbers use the binary code 0000, 0001, 0010, c, 1001. The decimal value
is exactly the same

Question 5

BCD addition

Answer 5

As long as the sum is below or equal to 9, we are good. But then
9+9+ 1(carry) = 19. (Max value, out of BCD range)

We add BCD by
1. Adding them like binary if it’s greater than or equal to 10 then we add (0110)2.
As
This is because a carry in the most significant bit
position of the binary sum and a decimal carry differ by 16 - 10 = 6.