|1-7||Express the following numbers in decimal: (10110.0101)2, (16.5)16, and (26.24)8.|
|1-10||Convert the decimal number 345 to binary in two ways: (a) convert directly to binary; (b) convert first to hexadecimal, then from hexadecimal to binary. Which method is faster?|
|1-18|| Perform subtraction on the following unsigned binary numbers
using the 2's-complement of the subtrahend. Where the result
should be negative, 2's complement it and affix a minus sign.|
(a) 11011 - 11001 (b) 110100 - 10101 (c) 1011 - 110000 (d) 101010 - 101011
|2-3|| Simplify the following Boolean expressions to a minimum number
(a) ABC + A'B + ABC'
(b) x'yz + xz
(c) (x+y)'(x' + y')
(d) xy + x(wz + wz')
(e) (BC' + A'D)(AB' + CD')
|2-16|| Express the following function in sum of minterms and
product of maxterms:
F(A, B, C, D) = B'D + A'D + BD
|3-5|| Simplify the following Boolean functions, using four-variable maps:
(a) F(w, x, y, z) = Σ (1, 4, 5, 6, 12, 14, 15)
(b) F(A, B, C, D) = Σ (0, 1, 2, 4, 5, 7, 11, 15)
(c) F(w, x, y, z) = Σ (2, 3, 10, 11, 12, 13, 14, 15)
|3-13|| Simplify the following expressions in (1) sum of products and
(2) products of sums:
(a) x'z' + y'z' + yz' + xy
(b) AC' + B'D + A'CD + ABCD
(c) (A' + B' + D')(A + B' + C')(A' + B + D') (B + C' + D')
|3-20||Draw the multiple-level NAND circuit for the following expression: (AB'+CD')E + BC(A+B)|
|3-24||Implement the following Boolean function F, using the two-level forms (a) NAND-AND, (b) AND-NOR, (c) OR-NAND, and (d) NOR-OR: F(A,B,C,D)=Σ (0, 1, 2, 3, 4, 8, 9, 12)|
|3-25||List the eight degenerate two-level forms and show that they reduce to a single operation. Explain how the degenerate two-level forms can be used to extend the number of inputs to a gate.|
|4-1|| Consider the combinational circuit shown in Fig. P4-1
(a) Derive the Boolean expressions for T1 through T4. Evaluate the outputs F1 and F2 as a function of the four inputs.
(b) List the truth table with 16 binary combinations of the four input variables. Then list the binary values for T1 through T4 and outputs F1 and F2 in the table.
|4-7||Design a combinational circuit that converts a 4-bit Gray code (Table 1-6) to a 4-bit binary number. Implement the circuit with exclusive-OR gates.|
|4-12|| (a) Design a half-subtractor circuit with inputs x and y and outputs D
and B. The circuit subtracts the bits x - y and places the difference
in D and the borrow in B.
(b) Design a full-subtractor circuit with three inputs x, y, z and two outputs D and B. The circuit subtracts x - y - z, where z is the input borrow, B is the output borrow, and D is the difference.
|4-28|| A combinational circuit is defined by the following three Boolean
F1 = x'y'z' + xz
F2 = xy'z' + x'y
F3 = x'y'z + xy
Design the circuit with a decoder and external gates.
|4-33||Implement a full adder with two 4x1 multiplexers.|