# COMP 273 Assignment 1

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## Description

1 Number Representation, 2s Complement, and Floating Point
Show your work in writing up answers to the following questions to get full credit.
1. Convert positional notation 0.1010112 from binary to decimal using any appropriate algorithm that was seen in class.
2. Convert positional notation 6.7510 from decimal to binary and hexadecimal using algorithms that were seen in class.
3. Convert positional notation 1FA.U06G32 from base 32 to binary and then to hexadecimal.
Here, much like base 16, we use letters A through V to represent 10 through 31, and note
the fractional part in this case is U zero six G (i.e., it is difficult to see the difference between
0 and O). Use the shortcut of grouping binary bits as seen in class.
4. Convert the base 5 number 30310045 to hexadecimal.
5. Represent the base 10 number −412878610 as a 24 bit signed binary number using two’s
symbols.
6. Now that you’ve worked up an appetite for number conversions, represent -2.625 as an
2 Seven Segment Decoder
A seven segment decoder is typically used to determine which light emitting diodes in a seven segment display should illuminate to display a
digit specified in binary coded decimal.
Logisim includes such a seven segment display that you will use in this
question. The decoder takes as input four binary bits, which we label
in order from most significant bit to least significant bit, A3 A2 A1 A0.
The decoder produces as output a pattern of 7 bits, S6 S5 S4 S3 S2 S1
S0, which specifies which segments should illuminate. The figure on the
right shows the relationship between the pins and the corresponding segments of the display. Note that there is an 8th pin, S7, which controls the
decimal point and that we will not use in this assignment.