Computer Science Department

College of Arts and Sciences

CS-101(B1) / Fall 1997

Give the truth table for the 3-input ``equivalence'' circuit
(also known as the ``unanimous'' circuit),
which is defined as follows.. It accepts three inputs **W**, **X**, and
**Y** and produces one output **Z**. The output of the circuit should be
1 only when **W**, **X**, and **Y** are the same (i.e. all three are 0 or
all three are 1).

Using the truth table you obtained in the previous question, construct a
logical circuit (using only `AND`, `OR`, and `NOT` gates)
that implements the 3-input ``equivalence'' circuit.

Let `A` and `B` be two bytes, where `A = 01101011`
and `B = 00111011`. What is the decimal value of `A`? What is
the decimal value of `B`? Perform an addition of
`A` and `B` in binary showing the sum and carry for each
bit. What is the decimal value of the sum?
Does it check with the sum of the decimal values of `A` and `
B`?

Give the representation of the decimal number **176** in binary (radix = 2),
in ternary (radix = 3), and in octal (radix = 8). How many digits
would you need to represent the number **1234** in hexadecimal (radix = 16)?

Show the truth table for the ``sum'' function and the ``carry''
function for the full adder described in class. Draw a diagram for a
circuit to add 3-bit numbers using 3 full adders.

Created on: 1997.11.13 Updated on: 1997.11.13 Maintainer: Azer Bestavros best@cs.bu.edu