PROBLEMS 327(b) (1011010) 2
(c) (.110101) 2
(d) (100101111011.01011) 2
(e) (1110110111.1011) 2
6.1.7Convert the following hexadecimal numbers into
decimal numbers:
(a) (6B) 16
(b) (1F4) 16
(c) (C59) 16
(d) (256.72) 16
(e) (.0E3) 16*6.1.8Convert the following decimal numbers into hex-
adecimal numbers:
(a) (97) 10
(b) (864) 10
(c) (5321) 10
(d) (0.00125) 10
(e) (449.375) 10
6.1.9Convert the following binary numbers into hex-
adecimal numbers:
(a) (11101110100100.100111) 2
(b) (1011011101) 2
(c) (.11101) 2
(d) (1101110001.11011110) 2
(e) (.0000110111000101) 2
6.1.10Convert the following hexadecimal numbers into
binary numbers:
(a) (2ABF5) 16
(b) (3BA4.9C) 16
(c) (0.0DC5) 16
(d) (15CE.FB3) 16
(e) (2AB.F8) 16
6.1.11Convert the following decimal numbers into BCD
numbers:
(a) (567) 10
(b) (1978) 10
(c) (163.25) 10
(d) (0.659) 10
(e) (2153.436) 10
6.1.12Convert the following BCD numbers into decimal
numbers:
(a) (010101100111)BCD
(b) (.011001011001)BCD
(c) (.100110000100)BCD
(d) (10010010.00000001)BCD
(e) (0010000101010011.010000110110)BCD
*6.1.13Obtain the truth table for the logic block shown in
Figure P6.1.13.
6.1.14Find the output functionYfor the logic circuits of
Figure P6.1.14 (a) and (b).
6.1.15An AOI (AND-OR-INVERT) gate is shown in
Figure P6.1.15 with its two possible realizations.
Obtain the output functionYand show that the two
circuits are equivalent.
6.1.16Figure P6.1.16(a) shows the seven-segment array
that is widely used to form the decimal digits 0 to 9
in LED displays, as indicated in Figure P6.1.16(b).
Let the inputs be the four binary digits used to
represent the decimal digits 0 to 9. (a) For the
segmentY 1 , (b) For the segmentY 2 , and (c) For
the segmentY 3 to be turned on, develop the logic
expression and find one possible logic circuit to
realize the output in each case.
6.1.17The DeMorgan’s theorems suggest that the basic
logic operations can be realized by use of inverters
and NAND gates only. For the circuits shown in
Figure P6.1.17, find the truth table, the type of gate
realized, and the expression for the logic output,
in each case.
6.1.18For the NOR and inverter realizations shown in
Figure P6.1.18, find the truth table, the type of gate
realized, and the expression for the logic output,
in each case.
*6.1.19Obtain the Boolean expressions for the logic cir-
cuits shown in Figure P6.1.19.
6.1.20Draw the logic diagram for the following Boolean
expressions (without any simplification).
(a)Y=AB+BC ̄
(b)Y=(A+B)(A ̄+C)
(c)Y=A·B+B ̄·C+A·B·D+A·C·D(d)Y=(A ̄+B)·(A+C) ̄ ·(B+C)
6.1.21Obtain the Boolean expressions for the logic cir-
cuits shown in Figure P6.1.21.
6.1.22Using Boolean identities, simplify the following:
(a)Y=A+A ̄·B