Digit Logic & Computer Systems
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EEL 3701C - Digit Logic & Computer Systems
Homework 3
72 pts
Problem I (Encoder, Decoder, 11pts)
1) Show how to make the 8-to-3 priority encoder representing the picture below using two 4-to-2
priority encoders and any additional necessary gates (5 pts)
2) Realize a full subtracter using a 3-to-8 line decoder with inverting outputs and
a) two NAND gates (3 pts)
b) two AND gates (3 pts)
Problem II (Memory, 15 pts)
1. Using a graphic explain the following memory technology: mask-programmed ROM, PROM, EPROM,
EEPROM, EEPROM, FLAS, RAM, SRAM, DRAM (9 pts)
2. Sketch the internal design of a 8 × 3 ROM with the following: value 2 is stored at address 1, value 5
store at address 5, value 1 store at address 0 and value 0 stored at all remaining addresses. (2 pts)
3. Compose 1kx8 ROM’s into an 8kx8 ROM (2 pts)
4. Show how to use a 1kx8 ROM to implement a 512x6 ROM (2 pts)
Problem III (Arithmetic, 14 pts)
1. Use the shift and add algorithm to perform the following multiplications
• 15x66 (2 pts)
• (-55) x (-35) (3 pts)
• 40 x (-16) (3 pts)
2. Use the restoring algorithm to perform the following divisions
• 58/13 (3 pts)
• 85/27 (3 pts)
Problem IV (Microprogramming, 17 Pts)
The circuit below counts the number of 1’s in an input A. Assume A is available when a start signal s
becomes 1; A is loaded into a parallel loading shift register. At the same time a value is loaded into an
up-counter C. After completing the count of 1’s, the controller generates a signal Done until s has
returned to 0. (Note that the serial input to R, ai, can be a constant value.)
For the shift register: For a right shift Sh = 1, Ld = 0 or Ld = 1. For a left shift, Sh = 0 , Ld = 1
For the counter: Load Ld = 1, IncC = 1 count up
1) Specify the value to be loaded into C (2 Pts).
2) Design the controller as microprogrammed unit (15 Pts).
Problem V (Assembler Programing with SPIM, 15 Pts)
Use the SPIM simulator to compile and run your assembler program of Exercise 5. A guide for executing
and debugging programs in the SPIM environment is provided on canvas.