When Selenite children, who have only 4 fingers (the middle finger, the ring finger, the little finger and the thumb), learn to count on the fingers, the notion of order is not their priority. This has the consequence that, for them, raising the middle and ring fingers at the same time or the little finger and the thumb produces the same result, namely here the representation of the number 2. If they raise their thumb simultaneously, the middle finger and the little finger or the ring finger, the thumb and the middle finger this will represent for them the same number, namely 3. You have been asked here to make a circuit which has 4 bits as input representing the 4 fingers of the hand of 'a selenite child and at the output N bits encoding the information represented by these fingers in base 2. A bit at the input of the circuit is at 1 when the corresponding finger is raised, otherwise it is at 0. (a) Determine the number N of bits required at the output of the circuit. (b) Draw up the truth table(s) carrying out this coding. (c) Using Karnaugh tables, determine the minimum Boolean equations of all outputs of the circuit. (d) Draw the circuit diagram.
When Selenite children, who have only 4 fingers (the middle finger, the ring finger, the little finger and the thumb), learn to count on the fingers, the notion of order is not their priority. This has the consequence that, for them, raising the middle and ring fingers at the same time or the little finger and the thumb produces the same result, namely here the representation of the number 2. If they raise their thumb simultaneously, the middle finger and the little finger or the ring finger, the thumb and the middle finger this will represent for them the same number, namely 3. You have been asked here to make a circuit which has 4 bits as input representing the 4 fingers of the hand of 'a selenite child and at the output N bits encoding the information represented by these fingers in base 2. A bit at the input of the circuit is at 1 when the corresponding finger is raised, otherwise it is at 0. (a) Determine the number N of bits required at the output of the circuit. (b) Draw up the truth table(s) carrying out this coding. (c) Using Karnaugh tables, determine the minimum Boolean equations of all outputs of the circuit. (d) Draw the circuit diagram.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercise 3: Finger to Binary
When Selenite children, who have only 4 fingers (the middle finger, the ring
finger, the little finger and the thumb), learn to count on the fingers, the notion of
order is not their priority. This has the consequence that, for them, raising the middle
and ring fingers at the same time or the little finger and the thumb produces the same
result, namely here the representation of the number 2. If they raise their thumb
simultaneously, the middle finger and the little finger or the ring finger, the thumb and
the middle finger this will represent for them the same number, namely 3. You have
been asked here to make a circuit which has 4 bits as input representing the 4 fingers
of the hand of 'a selenite child and at the output N bits encoding the information
represented by these fingers in base 2. A bit at the input of the circuit is at 1 when the
corresponding finger is raised, otherwise it is at 0.
(a) Determine the number N of bits required at the output of the circuit.
(b) Draw up the truth table(s) carrying out this coding.
(c) Using Karnaugh tables, determine the minimum Boolean equations of all outputs of
the circuit.
(d) Draw the circuit diagram.
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