implement a 2-input (A, B), 3-output (C, D, E) circuit which behaves the following way:
Inputs Outputs
A B C D E
0 0 1 0 0
1 0 0 1 0
0 1 1 1 0
1 1 0 0 1
(This circuit increments — adds 1 to — the two-bit input AB, producing a 3-bit output CDE.)
Using any gates you like, implement a 2-input (A, B), 2-output (Q, C) circuit which behaves in the following way:
Inputs Outputs
A B Q C
0 0 0 0
1 0 1 0
0 1 1 0
1 1 0 1
This is known as a half-adder: it “adds” together two bits (A and B) and produces the sum on output Q; if the sum is too large to fit in a single bit (i.e., if A and B are both 1, and the sum is 2) then Q is 0 and the carry output C is 1. A half-adder is a building block to building an addition circuit.
Using any gates you like, implement a 2-input, 2-output circuit which behaves the following way:
Inputs Outputs
A B Q R
0 0 0 0
1 0 1 0
0 1 1 1
1 1 0 0
This is a half-subtractor circuit, computing the 1-bit subtraction A - B; the R output is the borrow output; if A < B then the subtraction cannot be performed without borrowing from a higher bit.