Binary Addition/Subtraction

Question 1

What are the boolean algebraic formula for the output of a 2-input half adder?

Answer 1

Carry = A . B

Sum = A XOR B

Question 2

What is the difference between a half adder and a full adder?

Answer 2

A full adder has a Carry In in addition.

Question 3

What are the boolean algeberaic formulae for the output of a full adder?

Answer 3

Sum = A XOR B XOR C_IN

Carry_OUT = A.B + A.C_IN + B.C_IN

Question 4

Draw the symbolic box diagram for a 2 input Full Adder showing all inputs and outputs

Answer 4

Question 5

Draw the box diagram showing how to connect full adders to add together two 4-bit numbers

Answer 5

Question 6

How do you calculate the propagation delay for a ripple carry adder?

Answer 6

Question 7

Draw the truth table for a full adder, mentioning carry status at each line.

Answer 7

Question 8

How do we subtract two numbers using full adders?

Answer 8

A + (-B)

We take the 2’s complement of B and add with A

We wary of overflow and underflow

Question 9

How do we detect overflow when dealing with subtraction/ 2’s complement?

Answer 9

Overflow if the carry out is different to the carry in

Overflow = C_IN XOR C_OUT

Question 10

Draw a 4-bit subtracter

Answer 10

Question 11

Using XOR gates and a bit_invert signal show how you can design one circuit that can add or subtract two 4-bit numbers.

Answer 11