1. For each 8 BIT binary pattern shown in the table below please write corresponding values of the following interpretations: UNSIGNED INT, SIGNED INT, UNSIGNED Fixed Point, SIGNED Fixed Point.
Each correctly answered column is 2.5 points. FIXED POINT IS LOCATED TWO POSITIONS FROM THE LEFT! MOST SIGNIFICANT BIT IS 7. LEAST SIGNIFICANT BIT IS 0.
76543210
10000000 10000011 10000001 01000001 01111111 11111111 11111100 00000000 01111110 10001110 00010011
UNSIGNED INT
SIGNED INT
UNSIGNED Fixed Point
SIGNED Fixed Point
19
+19
4 + 3 = 16 + 3
44 44
+4 + 3 = + 19
Fixed Point
- What is the most negative number (largest absolute value negative) that can be represented using 16 bit signed integer representation? Please circle around over all the correct ones: -32768, -65536, -16384, -32767, NONE
- Please subtract two number in Hex. Then convert each operand to binary and perform the same operation in binary, then repeat BASE 10. The signed integers are represented using two’s complement.
0x0E —
0xFF
Result: 0x 0000 0000b dec:
Last NAME: First Name:
4.
Determine the MINIMAL number of bits required to represent -127.75 using:
4.1 ASCII code bits 4.2 (5 points) Binary Fixed Point representation
(please write the number of bits in the cell)
Fixed Point
4.3 Take the result from you answer in 4.2 and shift fixed point by 2 positions to the RIGHT. Please write down the resulting signed decimal value,
And the corresponding binary Fixed Point representation here.
00 00000000 00 0
4.4 Please write down the signed rational number stored in the 9-bit word below: 100000001
Fixed Point
5. Please determine if single precision floating point representation given below is NAN,or +Infinity,- Infinity, or a valid number floating point : The top row shows the bit index. PLEASE JUSTIFY your ANSWER and SHOW your work! Just the final result will not count as a correct answer.
01000000111000000000000000000000
6. Please determine the decimal value (scientific notation) of the single precision floating point representation given below: The top row shows the bit index. PLEASE SHOW your work! Just the final result will not count as correct answer. If it represents NAN, or Infinity, or zero please state this and justify.
bits (please write the number of bits in the cell) 0000000000 00 0
And the corresponding binary Fixed Point representation here.
|
3 1 |
3 0 |
2 9 |
2 8 |
2 7 |
2 6 |
3 5 |
2 4 |
2 3 |
2 2 |
2 1 |
2 0 |
1 9 |
1 8 |
1 7 |
1 6 |
1 5 |
1 4 |
1 3 |
1 2 |
1 1 |
1 0 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
|
3 1 1 |
3 0 1 |
2 9 0 |
2 8 0 |
2 7 0 |
2 6 0 |
3 5 1 |
2 4 0 |
2 3 1 |
2 2 1 |
2 1 1 |
2 0 1 |
1 9 1 |
1 8 1 |
1 7 1 |
1 6 1 |
1 5 1 |
1 4 0 |
1 3 0 |
1 2 0 |
1 1 0 |
1 0 0 |
9 0 |
8 0 |
7 0 |
6 0 |
5 0 |
4 0 |
3 0 |
2 0 |
1 0 |
0 0 |
Last NAME: First Name:
7. Please determine the decimal value (scientific notation) of the single precision floating point representation given below: The top row shows the bit index. PLEASE SHOW your work! Just the final result will not count as correct answer. If it represents NAN, or Infinity, or zero please state this and justify.
00000000000000000000000000000000
8. Please determine the decimal value (scientific notation) of the single precision floating point representation given below: The top row shows the bit index. PLEASE SHOW your work! Just the final result will not count as correct answer. If it represents NAN, or Infinity, or zero please state this and justify.
11111111111111111111111111111111
|
3 1 |
3 0 |
2 9 |
2 8 |
2 7 |
2 6 |
3 5 |
2 4 |
2 3 |
2 2 |
2 1 |
2 0 |
1 9 |
1 8 |
1 7 |
1 6 |
1 5 |
1 4 |
1 3 |
1 2 |
1 1 |
1 0 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
|
3 1 |
3 0 |
2 9 |
2 8 |
2 7 |
2 6 |
3 5 |
2 4 |
2 3 |
2 2 |
2 1 |
2 0 |
1 9 |
1 8 |
1 7 |
1 6 |
1 5 |
1 4 |
1 3 |
1 2 |
1 1 |
1 0 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
Last NAME: First Name:
In EACH Questions 10.1-10.4 you are given SIGNED Integers stored in 32 BIT Registers. (Not 33-BIT Register ). Please write decimal, and binary operands and the results. For each question you have to write the result and overflow or No overflow. You may override ‘0’ with ‘1’.
10.1 What is the result (hexadecimal, decimal and binary) of the following addition:
0x0000000E +
0xFFFFFFFF
HEX: 0x Decimal: Binary:0000 0000 0000 0000 0000 0000 0000 0000 ——————————————————————————————————————————————————-
10.2 (5 points) What is the result (hexadecimal, decimal and binary) of the following subtraction: 0x7FFFFFFF
–
0xFFFFFFFF
0x0000000000 Decimal: Binary: 00000000000000000000000000000000000 ——————————————————————————————————————————————————-
10.3 What is the result(hexadecimal, decimal and binary) of the following subtraction:
0x80000000
–
HEX:
HEX:
0xFFFFFFFF
0x Decimal: Binary: 00000000000000000000000000000000000
—————————————————————————————————————————————————– 10.4 (5 points) What is the result(hexadecimal, decimal and binary) of the following addition:
0X7FFFFFFF
+
0XFFFFFFFF
HEX: 0X Decimal: Binary
Please write your result in the following form:
0x80000000
+
OVEREFLOW
Decimal:+231-1 Binary: 01111111111111111111111111111111
