Download Boolean Function Simplification and Digital Circuit Design and more Essays (high school) Mathematics in PDF only on Docsity!
ECE-223, Solutions for Assignment
Chapter 3, Digital Design, M. Mano, 3rd^ Edition
3.3) Simplify the following Boolean functions, using three-variable maps: a) xy + x′y′z′ + x′yz′ b) x′y′ + yz + x′yz′ c) A′B + BC′ + B′C′
a) b)
xy+x′z′ x′+yz
c) C′ + A′B
3.5) Simplify the following Boolean functions, using four-variable maps: a) F(w, x, y, z) = ∑ (1, 4, 5, 6, 12, 14, 15) b) F(A, B, C, D) = ∑ (0, 1, 2, 4, 5, 7, 11, 15) c) F(w, x, y, z) = ∑ (2, 3, 10, 11, 12, 13, 14, 15) d) F(A, B, C, D) = ∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)
a) b)
w′y′z + xz′ + wxy 1) ACD + A′C′ + A′B′D′ + BCD
- ACD + A′C′ + A′B′D′ + A′BD
c) d)
wx + x′y BD + B′D′ + A′B
3.12) Simplify the following Boolean functions in products of sums: a) F(w, x, y, z) = ∑ (0, 2, 5, 6, 7, 8, 10) b) F(A, B, C, D) = ∏ (1, 3, 5, 7, 13, 15)
a) b)
F′ = wx + x′z + xy′z′ F′ = BD+ A′D F = (w′ + x′) (x + z′)(x′ + y + z) F = (B′+D′)(A+D′)
3.15) Simplify the following Boolean function F , together with the don’t-care conditions d , and then express the simplified function in sum of minterms: a) F(x, y, z) = ∑ (0, 1, 2, 4, 5) , d(x, y, z) = ∑(3, 6, 7) b) F(A, B, C, D) = ∑ (0, 6, 8, 13, 14), d(A, B, C, D) = ∑ (2, 4, 10) c) F(A, B, C, D) = ∑ (1,3,5,7,9,15), d(A, B, C, D) = ∑ (4,6,12,13)
a) F = 1 = ∑ (0, 1, 2, 3, 4, 5, 6, 7)
b) F = B′D′ + CD′ + ABC′D = ∑ (0, 2, 6, 8, 10, 13, 14)
c)
F = A′D + BD + C′D
x
y
z
P
x
y
z
C
P
3.16) Simplify the following expressions, and implement them with two-level NAND gate circuits: a) AB′ + ABD + ABD′ + A′C′D′ + A′BC′ b) BD + BCD′ + AB′C′D′
a) b)
F = A + BC′ + C′D′ F = BD + BC + AB′C′D′
3.28) Derive the circuits for a three-bit parity generator and four-bit parity checker using odd parity bit.
Same as Parity generator described in pages 97-99, Digital Design, M. Mano, 3 rd^ edition
