https://github.com/smoke-y/tinyalu
ALU that can add, sub, mul, div, and logically compare integer and floats
https://github.com/smoke-y/tinyalu
alu hardware verilog
Last synced: 2 months ago
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ALU that can add, sub, mul, div, and logically compare integer and floats
- Host: GitHub
- URL: https://github.com/smoke-y/tinyalu
- Owner: smoke-y
- Created: 2024-09-16T11:43:05.000Z (9 months ago)
- Default Branch: main
- Last Pushed: 2024-11-14T06:49:34.000Z (7 months ago)
- Last Synced: 2024-12-03T22:19:53.117Z (6 months ago)
- Topics: alu, hardware, verilog
- Language: Verilog
- Homepage:
- Size: 25.4 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# tinyalu
32-bit alu that can add, sub, div, mul and compare integers and IEEE-754 floating point numbers.
## IEEE-754
This is a method for representing floating point numbers.
```
(32 bit)
sign: 1 bit
exponent: 8 bit
mantissa: 23 bit
```
### sign
Float is positive if sign is 0, else negative.
### exponent
$$
IEEEexponent = exponent + bias
$$
for 32 bit, bias = 127
Bias is used to shift the representation of digits. If we are using 2's compliment, the list of possible numbers with given bits(n), starts with positive values. If the bias is $$ 2^{n-1} - 1$$ then the list will start with negative numbers. This allows ALU's to use their unsigned int comperator while comparing the mantissas of 2 floats. No additional circuitry is required.
```
BIN DEC 2S BIAS(bias=3)
000 0 0 -3
001 1 1 -2
010 2 2 -1
011 3 3 0
100 4 -4 1
101 5 -3 2
110 6 -2 3
111 7 -1 4
```
### mantissa
$$
23.5 = 10111.01001100
= 1.011101001100 * 2^4
$$
If we drop the leading 1(before the decimal) and take the part which is after the decimal, we get the mantissa.
NOTE: Mantissa assumes a leading 1.
$$
(-1)^{sign}*(1.mantissa)*2^{exponent-127}
$$
## ALU
ALU takes 3 inputs, 2 numbers and 1 instruction. It outputs a number and ZE(set to high when division by zero).
```
.... E D C B A
CBA: represents the operation
000: add
001: sub
011: mul
111: div
110: grt
100: equal
101: less
D: float if set, else int(input)
E: signed if set, else unsigned(input)
don't care if D is set
```